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Interactions Between Homotopy Theory And Algebra
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Author :Summer School on Interactions between Homotopy Theory and Algebra Publisher :American Mathematical Soc. ISBN 13 :0821838148 Total Pages :352 pages Book Rating :4.8/5 (218 download)
Book Synopsis Interactions between Homotopy Theory and Algebra by : Summer School on Interactions between Homotopy Theory and Algebra
Download or read book Interactions between Homotopy Theory and Algebra written by Summer School on Interactions between Homotopy Theory and Algebra and published by American Mathematical Soc.. This book was released on 2007 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on talks presented at the Summer School on Interactions between Homotopy theory and Algebra held at the University of Chicago in the summer of 2004. The goal of this book is to create a resource for background and for current directions of research related to deep connections between homotopy theory and algebra, including algebraic geometry, commutative algebra, and representation theory. The articles in this book are aimed at the audience of beginning researchers with varied mathematical backgrounds and have been written with both the quality of exposition and the accessibility to novices in mind.
Book Synopsis Rational Homotopy Theory by : Yves Felix
Download or read book Rational Homotopy Theory written by Yves Felix and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rational homotopy theory is a subfield of algebraic topology. Written by three authorities in the field, this book contains all the main theorems of the field with complete proofs. As both notation and techniques of rational homotopy theory have been considerably simplified, the book presents modern elementary proofs for many results that were proven ten or fifteen years ago.
Book Synopsis Homotopy of Operads and Grothendieck-Teichmuller Groups by : Benoit Fresse
Download or read book Homotopy of Operads and Grothendieck-Teichmuller Groups written by Benoit Fresse and published by American Mathematical Soc.. This book was released on 2017-05-22 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ultimate goal of this book is to explain that the Grothendieck–Teichmüller group, as defined by Drinfeld in quantum group theory, has a topological interpretation as a group of homotopy automorphisms associated to the little 2-disc operad. To establish this result, the applications of methods of algebraic topology to operads must be developed. This volume is devoted primarily to this subject, with the main objective of developing a rational homotopy theory for operads. The book starts with a comprehensive review of the general theory of model categories and of general methods of homotopy theory. The definition of the Sullivan model for the rational homotopy of spaces is revisited, and the definition of models for the rational homotopy of operads is then explained. The applications of spectral sequence methods to compute homotopy automorphism spaces associated to operads are also explained. This approach is used to get a topological interpretation of the Grothendieck–Teichmüller group in the case of the little 2-disc operad. This volume is intended for graduate students and researchers interested in the applications of homotopy theory methods in operad theory. It is accessible to readers with a minimal background in classical algebraic topology and operad theory.
Book Synopsis Building Bridges Between Algebra and Topology by : Wojciech Chachólski
Download or read book Building Bridges Between Algebra and Topology written by Wojciech Chachólski and published by Birkhäuser. This book was released on 2018-03-31 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an elaborated version of lecture notes for two advanced courses: (Re)Emerging methods in Commutative Algebra and Representation Theory and Building Bridges Between Algebra and Topology, held at the CRM in the spring of 2015. Homological algebra is a rich and ubiquitous area; it is both an active field of research and a widespread toolbox for many mathematicians. Together, these notes introduce recent applications and interactions of homological methods in commutative algebra, representation theory and topology, narrowing the gap between specialists from different areas wishing to acquaint themselves with a rapidly growing field. The covered topics range from a fresh introduction to the growing area of support theory for triangulated categories to the striking consequences of the formulation in the homotopy theory of classical concepts in commutative algebra. Moreover, they also include a higher categories view of Hall algebras and an introduction to the use of idempotent functors in algebra and topology.
Book Synopsis Algebra, Algebraic Topology and their Interactions by : Jan-Erik Roos
Download or read book Algebra, Algebraic Topology and their Interactions written by Jan-Erik Roos and published by Springer. This book was released on 2006-11-14 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 982 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.
Book Synopsis Homotopy Theory via Algebraic Geometry and Group Representations by : Mark E. Mahowald
Download or read book Homotopy Theory via Algebraic Geometry and Group Representations written by Mark E. Mahowald and published by American Mathematical Soc.. This book was released on 1998 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: The academic year 1996-97 was designated as a special year in Algebraic Topology at Northwestern University (Evanston, IL). In addition to guest lecturers and special courses, an international conference was held entitled "Current trends in algebraic topology with applications to algebraic geometry and physics". The series of plenary lectures included in this volume indicate the great breadth of the conference and the lively interaction that took place among various areas of mathematics. Original research papers were submitted, and all submissions were refereed to the usual journal standards.
Book Synopsis Foundations of Stable Homotopy Theory by : David Barnes
Download or read book Foundations of Stable Homotopy Theory written by David Barnes and published by Cambridge University Press. This book was released on 2020-03-26 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The beginning graduate student in homotopy theory is confronted with a vast literature on spectra that is scattered across books, articles and decades. There is much folklore but very few easy entry points. This comprehensive introduction to stable homotopy theory changes that. It presents the foundations of the subject together in one place for the first time, from the motivating phenomena to the modern theory, at a level suitable for those with only a first course in algebraic topology. Starting from stable homotopy groups and (co)homology theories, the authors study the most important categories of spectra and the stable homotopy category, before moving on to computational aspects and more advanced topics such as monoidal structures, localisations and chromatic homotopy theory. The appendix containing essential facts on model categories, the numerous examples and the suggestions for further reading make this a friendly introduction to an often daunting subject.
Book Synopsis Rational Homotopy Theory II by : Yves Félix
Download or read book Rational Homotopy Theory II written by Yves Félix and published by World Scientific. This book was released on 2015-02-11 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph is a detailed account with complete proofs of rational homotopy theory for general non-simply connected spaces, based on the minimal models introduced by Sullivan in his original seminal article. Much of the content consists of new results, including generalizations of known results in the simply connected case. The monograph also includes an expanded version of recently published results about the growth and structure of the rational homotopy groups of finite dimensional CW complexes, and concludes with a number of open questions. This monograph is a sequel to the book Rational Homotopy Theory [RHT], published by Springer in 2001, but is self-contained except only that some results from [RHT] are simply quoted without proof. Contents:Basic Definitions and ConstructionsHomotopy Lie Algebras and Sullivan Lie AlgebrasFibrations and Λ-ExtensionsHolonomyThe Model of the Fibre is the Fibre of the ModelLoop Spaces and Loop Space ActionsSullivan SpacesExamplesLusternik-Schnirelmann CategoryDepth of a Sullivan Algebra and of a Sullivan Lie AlgebraDepth of a Connected Graded Lie Algebra of Finite TypeTrichotomyExponential GrowthStructure of a Graded Lie Algebra of Finite DepthWeight Decompositions of a Sullivan Lie AlgebraProblems Readership: Researchers in algebraic topology and Lie algebra theory.Key Features:Contains the basis for using rational homotopy theory for non-simply connected spacesContains new important information on the rational homotopy Lie algebra of spacesIs at the frontier of the research in rational homotopyKeywords:Rational Homotopy Theory;Algebraic Topology;Malcev Completion;Graded Lie Algebra
Author :Geometry and Their Interactions International Conference on Midwest Algebra Publisher :American Mathematical Soc. ISBN 13 :0821840940 Total Pages :270 pages Book Rating :4.8/5 (218 download)
Book Synopsis Algebra, Geometry and Their Interactions by : Geometry and Their Interactions International Conference on Midwest Algebra
Download or read book Algebra, Geometry and Their Interactions written by Geometry and Their Interactions International Conference on Midwest Algebra and published by American Mathematical Soc.. This book was released on 2007 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume's papers present work at the cutting edge of current research in algebraic geometry, commutative algebra, numerical analysis, and other related fields, with an emphasis on the breadth of these areas and the beneficial results obtained by the interactions between these fields. This collection of two survey articles and sixteen refereed research papers, written by experts in these fields, gives the reader a greater sense of some of the directions in which this research is moving, as well as a better idea of how these fields interact with each other and with other applied areas. The topics include blowup algebras, linkage theory, Hilbert functions, divisors, vector bundles, determinantal varieties, (square-free) monomial ideals, multiplicities and cohomological degrees, and computer vision.
Book Synopsis A Handbook of Model Categories by : Scott Balchin
Download or read book A Handbook of Model Categories written by Scott Balchin and published by Springer Nature. This book was released on 2021-10-29 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book outlines a vast array of techniques and methods regarding model categories, without focussing on the intricacies of the proofs. Quillen model categories are a fundamental tool for the understanding of homotopy theory. While many introductions to model categories fall back on the same handful of canonical examples, the present book highlights a large, self-contained collection of other examples which appear throughout the literature. In particular, it collects a highly scattered literature into a single volume. The book is aimed at anyone who uses, or is interested in using, model categories to study homotopy theory. It is written in such a way that it can be used as a reference guide for those who are already experts in the field. However, it can also be used as an introduction to the theory for novices.
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.
Book Synopsis Surveys on Recent Developments in Algebraic Geometry by : Izzet Coskun
Download or read book Surveys on Recent Developments in Algebraic Geometry written by Izzet Coskun and published by American Mathematical Soc.. This book was released on 2017-07-12 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.
Book Synopsis Algebraic Homotopy by : Hans J. Baues
Download or read book Algebraic Homotopy written by Hans J. Baues and published by Cambridge University Press. This book was released on 1989-02-16 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in topology and algebra are discussed, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful tools for homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group homotopy equivalences. Applications and examples of such computations are given, including when the fundamental group is non-trivial. Moreover, the deep connection between the homotopy classification problems and the cohomology theory of small categories is demonstrated. The prerequisites of the book are few: elementary topology and algebra. Consequently, this account will be valuable for non-specialists and experts alike. It is an important supplement to the standard presentations of algebraic topology, homotopy theory, category theory and homological algebra.
Book Synopsis Real Homotopy of Configuration Spaces by : Najib Idrissi
Download or read book Real Homotopy of Configuration Spaces written by Najib Idrissi and published by Springer Nature. This book was released on 2022-06-11 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a unified and accessible account of recent developments regarding the real homotopy type of configuration spaces of manifolds. Configuration spaces consist of collections of pairwise distinct points in a given manifold, the study of which is a classical topic in algebraic topology. One of this theory’s most important questions concerns homotopy invariance: if a manifold can be continuously deformed into another one, then can the configuration spaces of the first manifold be continuously deformed into the configuration spaces of the second? This conjecture remains open for simply connected closed manifolds. Here, it is proved in characteristic zero (i.e. restricted to algebrotopological invariants with real coefficients), using ideas from the theory of operads. A generalization to manifolds with boundary is then considered. Based on the work of Campos, Ducoulombier, Lambrechts, Willwacher, and the author, the book covers a vast array of topics, including rational homotopy theory, compactifications, PA forms, propagators, Kontsevich integrals, and graph complexes, and will be of interest to a wide audience.
Book Synopsis Rational Homotopy Type by : Wen-tsün Wu
Download or read book Rational Homotopy Type written by Wen-tsün Wu and published by Lecture Notes in Mathematics. This book was released on 1987-07-15 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive monograph provides a self-contained treatment of the theory of I*-measure, or Sullivan's rational homotopy theory, from a constructive point of view. It centers on the notion of calculability which is due to the author himself, as are the measure-theoretical and constructive points of view in rational homotopy. The I*-measure is shown to differ from other homology and homotopy measures in that it is calculable with respect to most of the important geometric constructions encountered in algebraic topology. This approach provides a new method of treatment and leads to various new results. In particular, an axiomatic system of I*-measure is formulated, quite different in spirit from the usual Eilenberg-Steenrod axiomatic system for homology, and giving at the same time an algorithmic method of computation of the I*-measure in concrete cases. The book will be of interest to researchers in rational homotopy theory and will provide them with new ideas and lines of research to develop further.
Book Synopsis Factorization Algebras in Quantum Field Theory by : Kevin Costello
Download or read book Factorization Algebras in Quantum Field Theory written by Kevin Costello and published by Cambridge University Press. This book was released on 2017 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume develops factorization algebras with a focus upon examples exhibiting their use in field theory, which will be useful for researchers and graduates.
