Bousfield Classes And Ohkawas Theorem

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Bousfield Classes and Ohkawa's Theorem

Author : Takeo Ohsawa
Publisher : Springer Nature
ISBN 13 : 9811515883
Total Pages : 438 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Bousfield Classes and Ohkawa's Theorem by : Takeo Ohsawa

Download or read book Bousfield Classes and Ohkawa's Theorem written by Takeo Ohsawa and published by Springer Nature. This book was released on 2020-03-18 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume originated in the workshop held at Nagoya University, August 28–30, 2015, focusing on the surprising and mysterious Ohkawa's theorem: the Bousfield classes in the stable homotopy category SH form a set. An inspiring, extensive mathematical story can be narrated starting with Ohkawa's theorem, evolving naturally with a chain of motivational questions: Ohkawa's theorem states that the Bousfield classes of the stable homotopy category SH surprisingly forms a set, which is still very mysterious. Are there any toy models where analogous Bousfield classes form a set with a clear meaning? The fundamental theorem of Hopkins, Neeman, Thomason, and others states that the analogue of the Bousfield classes in the derived category of quasi-coherent sheaves Dqc(X) form a set with a clear algebro-geometric description. However, Hopkins was actually motivated not by Ohkawa's theorem but by his own theorem with Smith in the triangulated subcategory SHc, consisting of compact objects in SH. Now the following questions naturally occur: (1) Having theorems of Ohkawa and Hopkins-Smith in SH, are there analogues for the Morel-Voevodsky A1-stable homotopy category SH(k), which subsumes SH when k is a subfield of C?, (2) Was it not natural for Hopkins to have considered Dqc(X)c instead of Dqc(X)? However, whereas there is a conceptually simple algebro-geometrical interpretation Dqc(X)c = Dperf(X), it is its close relative Dbcoh(X) that traditionally, ever since Oka and Cartan, has been intensively studied because of its rich geometric and physical information. This book contains developments for the rest of the story and much more, including the chromatics homotopy theory, which the Hopkins–Smith theorem is based upon, and applications of Lurie's higher algebra, all by distinguished contributors.

Homotopy Invariant Algebraic Structures

Author : Jean-Pierre Meyer
Publisher : American Mathematical Soc.
ISBN 13 : 082181057X
Total Pages : 392 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Homotopy Invariant Algebraic Structures by : Jean-Pierre Meyer

Download or read book Homotopy Invariant Algebraic Structures written by Jean-Pierre Meyer and published by American Mathematical Soc.. This book was released on 1999 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the conference held in honor of J. Michael Boardman's 60th birthday. It brings into print his classic work on conditionally convergent spectral sequences. Over the past 30 years, it has become evident that some of the deepest questions in algebra are best understood against the background of homotopy theory. Boardman and Vogt's theory of homotopy-theoretic algebraic structures and the theory of spectra, for example, were two benchmark breakthroughs underlying the development of algebraic $K$-theory and the recent advances in the theory of motives. The volume begins with short notes by Mac Lane, May, Stasheff, and others on the early and recent history of the subject. But the bulk of the volume consists of research papers on topics that have been strongly influenced by Boardman's work. Articles give readers a vivid sense of the current state of the theory of "homotopy-invariant algebraic structures". Also included are two major foundational papers by Goerss and Strickland on applications of methods of algebra (i.e., Dieudonné modules and formal schemes) to problems of topology. Boardman is known for the depth and wit of his ideas. This volume is intended to reflect and to celebrate those fine characteristics.

Axiomatic, Enriched and Motivic Homotopy Theory

Author : John Greenlees
Publisher : Springer Science & Business Media
ISBN 13 : 940070948X
Total Pages : 396 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Axiomatic, Enriched and Motivic Homotopy Theory by : John Greenlees

Download or read book Axiomatic, Enriched and Motivic Homotopy Theory written by John Greenlees and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The NATO Advanced Study Institute "Axiomatic, enriched and rna tivic homotopy theory" took place at the Isaac Newton Institute of Mathematical Sciences, Cambridge, England during 9-20 September 2002. The Directors were J.P.C.Greenlees and I.Zhukov; the other or ganizers were P.G.Goerss, F.Morel, J.F.Jardine and V.P.Snaith. The title describes the content well, and both the event and the contents of the present volume reflect recent remarkable successes in model categor ies, structured ring spectra and homotopy theory of algebraic geometry. The ASI took the form of a series of 15 minicourses and a few extra lectures, and was designed to provide background, and to bring the par ticipants up to date with developments. The present volume is based on a number of the lectures given during the workshop. The ASI was the opening workshop of the four month programme "New Contexts for Stable Homotopy Theory" which explored several themes in greater depth. I am grateful to the Isaac Newton Institute for providing such an ideal venue, the NATO Science Committee for their funding, and to all the speakers at the conference, whether or not they were able to contribute to the present volume. All contributions were refereed, and I thank the authors and referees for their efforts to fit in with the tight schedule. Finally, I would like to thank my coorganizers and all the staff at the Institute for making the ASI run so smoothly. J.P.C.GREENLEES.

Geometric and Topological Aspects of the Representation Theory of Finite Groups

Author : Jon F. Carlson
Publisher : Springer
ISBN 13 : 3319940333
Total Pages : 493 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Geometric and Topological Aspects of the Representation Theory of Finite Groups by : Jon F. Carlson

Download or read book Geometric and Topological Aspects of the Representation Theory of Finite Groups written by Jon F. Carlson and published by Springer. This book was released on 2018-10-04 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.

Stable Homotopy over the Steenrod Algebra

Author : John Harold Palmieri
Publisher : American Mathematical Soc.
ISBN 13 : 0821826689
Total Pages : 193 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Stable Homotopy over the Steenrod Algebra by : John Harold Palmieri

Download or read book Stable Homotopy over the Steenrod Algebra written by John Harold Palmieri and published by American Mathematical Soc.. This book was released on 2001 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title applys the tools of stable homotopy theory to the study of modules over the mod $p$ Steenrod algebra $A DEGREES{*}$. More precisely, let $A$ be the dual of $A DEGREES{*}$; then we study the category $\mathsf{stable}(A)$ of unbounded cochain complexes of injective comodules over $A$, in which the morphisms are cochain homotopy classes of maps. This category is triangulated. Indeed, it is a stable homotopy category, so we can use Brown representability, Bousfield localization, Brown-Comenetz duality, and other homotopy-theoretic tools to study it. One focus of attention is the analogue of the stable homotopy groups of spheres, which in this setting is the cohomology of $A$, $\mathrm{Ext}_A DEGREES{**}(\mathbf{F}_p, \mathbf{F}_p)$. This title also has nilpotence theorems, periodicity theorems, a convergent chromatic tower, and a nu

Mathematics Going Forward

Author : Jean-Michel Morel
Publisher : Springer Nature
ISBN 13 : 3031122445
Total Pages : 629 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Mathematics Going Forward by : Jean-Michel Morel

Download or read book Mathematics Going Forward written by Jean-Michel Morel and published by Springer Nature. This book was released on 2023-06-14 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an original collection of articles by 44 leading mathematicians on the theme of the future of the discipline. The contributions range from musings on the future of specific fields, to analyses of the history of the discipline, to discussions of open problems and conjectures, including first solutions of unresolved problems. Interestingly, the topics do not cover all of mathematics, but only those deemed most worthy to reflect on for future generations. These topics encompass the most active parts of pure and applied mathematics, including algebraic geometry, probability, logic, optimization, finance, topology, partial differential equations, category theory, number theory, differential geometry, dynamical systems, artificial intelligence, theory of groups, mathematical physics and statistics.

Groups, Geometry, and Dynamics

Author :
Publisher :
ISBN 13 :
Total Pages : 704 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Groups, Geometry, and Dynamics by :

Download or read book Groups, Geometry, and Dynamics written by and published by . This book was released on 2007 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publishes research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. Covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields.

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 888 pages
Book Rating : 4.X/5 (6 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2001 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Triangulated Categories

Author : Thorsten Holm
Publisher : Cambridge University Press
ISBN 13 : 1139488880
Total Pages : 473 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Triangulated Categories by : Thorsten Holm

Download or read book Triangulated Categories written by Thorsten Holm and published by Cambridge University Press. This book was released on 2010-06-24 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: A 2010 collection of survey articles by leading experts covering fundamental aspects of triangulated categories, as well as applications in algebraic geometry, representation theory, commutative algebra, microlocal analysis and algebraic topology. This is a valuable reference for experts and a useful introduction for graduate students entering the field.

Geometric Topology: Localization, Periodicity and Galois Symmetry

Author : Dennis P. Sullivan
Publisher : Springer
ISBN 13 : 9789048103508
Total Pages : 286 pages
Book Rating : 4.1/5 (35 download)

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Book Synopsis Geometric Topology: Localization, Periodicity and Galois Symmetry by : Dennis P. Sullivan

Download or read book Geometric Topology: Localization, Periodicity and Galois Symmetry written by Dennis P. Sullivan and published by Springer. This book was released on 2009-09-03 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The seminal ‘MIT notes’ of Dennis Sullivan were issued in June 1970 and were widely circulated at the time. The notes had a - jor in?uence on the development of both algebraic and geometric topology, pioneering the localization and completion of spaces in homotopy theory, including p-local, pro?nite and rational homotopy theory, le- ing to the solution of the Adams conjecture on the relationship between vector bundles and spherical ?brations, the formulation of the ‘Sullivan conjecture’ on the contractibility of the space of maps from the classifying space of a ?nite group to a ?nite dimensional CW complex, theactionoftheGalois groupoverQofthealgebraicclosureQof Q on smooth manifold structures in pro?nite homotopy theory, the K-theory orientation ofPL manifolds and bundles. Some of this material has been already published by Sullivan him- 1 self: in an article in the Proceedings of the 1970 Nice ICM, and in the 1974 Annals of Mathematics papers Genetics of homotopy theory and the Adams conjecture and The transversality character- 2 istic class and linking cycles in surgery theory . Many of the ideas originating in the notes have been the starting point of subsequent 1 reprinted at the end of this volume 2 joint with John Morgan vii viii 3 developments . However, the text itself retains a unique ?avour of its time, and of the range of Sullivan’s ideas.

Eco-friendly Polymer Nanocomposites

Author : Vijay Kumar Thakur
Publisher : Springer
ISBN 13 : 8132224736
Total Pages : 578 pages
Book Rating : 4.1/5 (322 download)

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Book Synopsis Eco-friendly Polymer Nanocomposites by : Vijay Kumar Thakur

Download or read book Eco-friendly Polymer Nanocomposites written by Vijay Kumar Thakur and published by Springer. This book was released on 2015-07-20 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains precisely referenced chapters, emphasizing environment-friendly polymer nanocomposites with basic fundamentals, practicality and alternatives to traditional nanocomposites through detailed reviews of different environmental friendly materials procured from different resources, their synthesis and applications using alternative green approaches. The book aims at explaining basics of eco-friendly polymer nanocomposites from different natural resources and their chemistry along with practical applications which present a future direction in the biomedical, pharmaceutical and automotive industry. The book attempts to present emerging economic and environmentally friendly polymer nanocomposites that are free from side effects studied in the traditional nanocomposites. This book is the outcome of contributions by many experts in the field from different disciplines, with various backgrounds and expertises. This book will appeal to researchers as well as students from different disciplines. The content includes industrial applications and will fill the gap between the research works in laboratory to practical applications in related industries.

Morava $K$-Theories and Localisation

Author : Mark Hovey
Publisher : American Mathematical Soc.
ISBN 13 : 0821810790
Total Pages : 114 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Morava $K$-Theories and Localisation by : Mark Hovey

Download or read book Morava $K$-Theories and Localisation written by Mark Hovey and published by American Mathematical Soc.. This book was released on 1999 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians working in group theory and generalizations.

Advances in Noncommutative Geometry

Author : Ali Chamseddine
Publisher : Springer Nature
ISBN 13 : 3030295974
Total Pages : 753 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Advances in Noncommutative Geometry by : Ali Chamseddine

Download or read book Advances in Noncommutative Geometry written by Ali Chamseddine and published by Springer Nature. This book was released on 2020-01-13 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23–April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.

Handbook of Nanofibers

Author : Ahmed Barhoum
Publisher : Springer
ISBN 13 : 9783319536545
Total Pages : 1300 pages
Book Rating : 4.5/5 (365 download)

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Book Synopsis Handbook of Nanofibers by : Ahmed Barhoum

Download or read book Handbook of Nanofibers written by Ahmed Barhoum and published by Springer. This book was released on 2019-09-10 with total page 1300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Handbook covers all aspects related to Nanofibers, from the experimental set-up for their fabrication to their potential industrial applications. It describes several kinds of nanostructured fibers such as metal oxides, natural polymers, synthetic polymers and hybrid inorganic-polymers or carbon-based materials. The first part of the Handbook covers the fundamental aspects, experimental setup, synthesis, properties and physico-chemical characterization of nanofibers. Specifically, this part details the history of nanofibers, different techniques to design nanofibers, self-assembly in nanofibers, critical parameters of synthesis, fiber alignment, modeling and simulation, types and classifications of nanofibers, and signature physical and chemical properties (i.e. mechanical, electrical, optical and magnetic), toxicity and regulations, bulk and surface functionalization and other treatments to allow them to a practical use. Characterization methods are also deeply discussed here. The second part of the Handbook deals with global markets and technologies and emerging applications of nanofibers, such as in energy production and storage, aerospace, automotive, sensors, smart textile design, energy conversion, tissue engineering, medical implants, pharmacy and cosmetics. Attention is given to the future of research in these areas in order to improve and spread the applications of nanofibers and their commercialization.

Equivariant Topology and Derived Algebra

Author : Scott Balchin
Publisher : Cambridge University Press
ISBN 13 : 1108931944
Total Pages : 357 pages
Book Rating : 4.1/5 (89 download)

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Book Synopsis Equivariant Topology and Derived Algebra by : Scott Balchin

Download or read book Equivariant Topology and Derived Algebra written by Scott Balchin and published by Cambridge University Press. This book was released on 2021-11-18 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of research papers, both new and expository, based on the interests of Professor J. P. C. Greenlees.

Handbook of Homotopy Theory

Author : Haynes Miller
Publisher : CRC Press
ISBN 13 : 1351251600
Total Pages : 1142 pages
Book Rating : 4.3/5 (512 download)

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Book Synopsis Handbook of Homotopy Theory by : Haynes Miller

Download or read book Handbook of Homotopy Theory written by Haynes Miller and published by CRC Press. This book was released on 2020-01-23 with total page 1142 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.

Axiomatic Stable Homotopy Theory

Author : Mark Hovey
Publisher : American Mathematical Soc.
ISBN 13 : 0821806246
Total Pages : 130 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Axiomatic Stable Homotopy Theory by : Mark Hovey

Download or read book Axiomatic Stable Homotopy Theory written by Mark Hovey and published by American Mathematical Soc.. This book was released on 1997 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: We define and investigate a class of categories with formal properties similar to those of the homotopy category of spectra. This class includes suitable versions of the derived category of modules over a commutative ring, or of comodules over a commutative Hopf algebra, and is closed under Bousfield localization. We study various notions of smallness, questions about representability of (co)homology functors, and various kinds of localization. We prove theorems analogous to those of Hopkins and Smith about detection of nilpotence and classification of thick subcategories. We define the class of Noetherian stable homotopy categories, and investigate their special properties. Finally, we prove that a number of categories occurring in nature (including those mentioned above) satisfy our axioms.