Foundational Essays On Topological Manifolds Smoothings And Triangulations

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Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88

Author : Robion C. Kirby
Publisher : Princeton University Press
ISBN 13 : 1400881501
Total Pages : 368 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88 by : Robion C. Kirby

Download or read book Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88 written by Robion C. Kirby and published by Princeton University Press. This book was released on 2016-03-02 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.

Foundational Essays on Topological Manifolds, Smoothings, and Triangulations

Author : Robion C. Kirby
Publisher : Annals of Mathematics Studies
ISBN 13 : 9780691081908
Total Pages : 355 pages
Book Rating : 4.0/5 (819 download)

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Book Synopsis Foundational Essays on Topological Manifolds, Smoothings, and Triangulations by : Robion C. Kirby

Download or read book Foundational Essays on Topological Manifolds, Smoothings, and Triangulations written by Robion C. Kirby and published by Annals of Mathematics Studies. This book was released on 1977 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.

From Topology to Computation: Proceedings of the Smalefest

Author : Morris W. Hirsch
Publisher : Springer Science & Business Media
ISBN 13 : 1461227402
Total Pages : 620 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis From Topology to Computation: Proceedings of the Smalefest by : Morris W. Hirsch

Download or read book From Topology to Computation: Proceedings of the Smalefest written by Morris W. Hirsch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extraordinary mathematical conference was held 5-9 August 1990 at the University of California at Berkeley: From Topology to Computation: Unity and Diversity in the Mathematical Sciences An International Research Conference in Honor of Stephen Smale's 60th Birthday The topics of the conference were some of the fields in which Smale has worked: • Differential Topology • Mathematical Economics • Dynamical Systems • Theory of Computation • Nonlinear Functional Analysis • Physical and Biological Applications This book comprises the proceedings of that conference. The goal of the conference was to gather in a single meeting mathemati cians working in the many fields to which Smale has made lasting con tributions. The theme "Unity and Diversity" is enlarged upon in the section entitled "Research Themes and Conference Schedule." The organizers hoped that illuminating connections between seemingly separate mathematical sub jects would emerge from the conference. Since such connections are not easily made in formal mathematical papers, the conference included discussions after each of the historical reviews of Smale's work in different fields. In addition, there was a final panel discussion at the end of the conference.

The Wild World of 4-Manifolds

Author : Alexandru Scorpan
Publisher : American Mathematical Society
ISBN 13 : 1470468611
Total Pages : 614 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Wild World of 4-Manifolds by : Alexandru Scorpan

Download or read book The Wild World of 4-Manifolds written by Alexandru Scorpan and published by American Mathematical Society. This book was released on 2022-01-26 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: What a wonderful book! I strongly recommend this book to anyone, especially graduate students, interested in getting a sense of 4-manifolds. —MAA Reviews The book gives an excellent overview of 4-manifolds, with many figures and historical notes. Graduate students, nonexperts, and experts alike will enjoy browsing through it. — Robion C. Kirby, University of California, Berkeley This book offers a panorama of the topology of simply connected smooth manifolds of dimension four. Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but small enough so that there is no room to undo the wildness. For example, only manifolds of dimension four can exhibit infinitely many distinct smooth structures. Indeed, their topology remains the least understood today. To put things in context, the book starts with a survey of higher dimensions and of topological 4-manifolds. In the second part, the main invariant of a 4-manifold—the intersection form—and its interaction with the topology of the manifold are investigated. In the third part, as an important source of examples, complex surfaces are reviewed. In the final fourth part of the book, gauge theory is presented; this differential-geometric method has brought to light how unwieldy smooth 4-manifolds truly are, and while bringing new insights, has raised more questions than answers. The structure of the book is modular, organized into a main track of about two hundred pages, augmented by extensive notes at the end of each chapter, where many extra details, proofs and developments are presented. To help the reader, the text is peppered with over 250 illustrations and has an extensive index.

Piecewise Linear Structures on Topological Manifolds

Author : Yuli RUDYAK
Publisher : World Scientific
ISBN 13 : 9814733792
Total Pages : 129 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Piecewise Linear Structures on Topological Manifolds by : Yuli RUDYAK

Download or read book Piecewise Linear Structures on Topological Manifolds written by Yuli RUDYAK and published by World Scientific. This book was released on 2015-12-28 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The study of triangulations of topological spaces has always been at the root of geometric topology. Among the most studied triangulations are piecewise linear triangulations of high-dimensional topological manifolds. Their study culminated in the late 1960s-early 1970s in a complete classification in the work of Kirby and Siebenmann. It is this classification that we discuss in this book, including the celebrated Hauptvermutung and Triangulation Conjecture. The goal of this book is to provide a readable and well-organized exposition of the subject, which would be suitable for advanced graduate students in topology. An exposition like this is currently lacking."--

The Disc Embedding Theorem

Author : Stefan Behrens
Publisher : Oxford University Press
ISBN 13 : 0192578383
Total Pages : 300 pages
Book Rating : 4.1/5 (925 download)

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Book Synopsis The Disc Embedding Theorem by : Stefan Behrens

Download or read book The Disc Embedding Theorem written by Stefan Behrens and published by Oxford University Press. This book was released on 2021-07-15 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on Fields medal winning work of Michael Freedman, this book explores the disc embedding theorem for 4-dimensional manifolds. This theorem underpins virtually all our understanding of topological 4-manifolds. Most famously, this includes the 4-dimensional Poincaré conjecture in the topological category. The Disc Embedding Theorem contains the first thorough and approachable exposition of Freedman's proof of the disc embedding theorem, with many new details. A self-contained account of decomposition space theory, a beautiful but outmoded branch of topology that produces non-differentiable homeomorphisms between manifolds, is provided, as well as a stand-alone interlude that explains the disc embedding theorem's key role in all known homeomorphism classifications of 4-manifolds via surgery theory and the s-cobordism theorem. Additionally, the ramifications of the disc embedding theorem within the study of topological 4-manifolds, for example Frank Quinn's development of fundamental tools like transversality are broadly described. The book is written for mathematicians, within the subfield of topology, specifically interested in the study of 4-dimensional spaces, and includes numerous professionally rendered figures.

The Collected Papers of Stephen Smale

Author : F Cucker
Publisher : World Scientific
ISBN 13 : 9814493058
Total Pages : 1740 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis The Collected Papers of Stephen Smale by : F Cucker

Download or read book The Collected Papers of Stephen Smale written by F Cucker and published by World Scientific. This book was released on 2000-06-30 with total page 1740 pages. Available in PDF, EPUB and Kindle. Book excerpt: '0Keywords:Differential Topology;Dynamical Systems;Economic Theory;Theory of Computation;Global Analysis;Stephen Smale“The three-volume collected works of S Smale are a very welcome addition to every mathematician''s book shelf and a must for a mathematics department library.”Mathematical Reviews'

The Collected Papers of Stephen Smale

Author : Stephen Smale
Publisher : World Scientific
ISBN 13 : 9789810249915
Total Pages : 532 pages
Book Rating : 4.2/5 (499 download)

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Book Synopsis The Collected Papers of Stephen Smale by : Stephen Smale

Download or read book The Collected Papers of Stephen Smale written by Stephen Smale and published by World Scientific. This book was released on 2000 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains one or two articles by world leaders on its subject which comment on the influence of Smale's work, and another article by Smale with his own retrospective views.

Algebraic and Geometric Topology

Author : R. James Milgram
Publisher : American Mathematical Soc.
ISBN 13 : 0821814338
Total Pages : 322 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic and Geometric Topology by : R. James Milgram

Download or read book Algebraic and Geometric Topology written by R. James Milgram and published by American Mathematical Soc.. This book was released on 1978 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains sections on Structure of topological manifolds, Low dimensional manifolds, Geometry of differential manifolds and algebraic varieties, $H$-spaces, loop spaces and $CW$ complexes, Problems.

A Morse-Bott Approach to Monopole Floer Homology and the Triangulation Conjecture

Author : Francesco Lin
Publisher : American Mathematical Soc.
ISBN 13 : 1470429632
Total Pages : 162 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A Morse-Bott Approach to Monopole Floer Homology and the Triangulation Conjecture by : Francesco Lin

Download or read book A Morse-Bott Approach to Monopole Floer Homology and the Triangulation Conjecture written by Francesco Lin and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present work the author generalizes the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped equipped with a structure which is isomorphic to its conjugate, the author defines the counterpart in this context of Manolescu's recent Pin(2)-equivariant Seiberg-Witten-Floer homology. In particular, the author provides an alternative approach to his disproof of the celebrated Triangulation conjecture.

Surgery on Compact Manifolds

Author : Charles Terence Clegg Wall
Publisher : American Mathematical Soc.
ISBN 13 : 0821809423
Total Pages : 321 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Surgery on Compact Manifolds by : Charles Terence Clegg Wall

Download or read book Surgery on Compact Manifolds written by Charles Terence Clegg Wall and published by American Mathematical Soc.. This book was released on 1999 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The publication of this book in 1970 marked the culmination of a period in the history of the topology of manifolds. This edition, based on the original text, is supplemented by notes on subsequent developments and updated references and commentaries.

Geometry and Topology of Manifolds

Author : Hans U. Boden
Publisher : American Mathematical Soc.
ISBN 13 : 9780821871492
Total Pages : 368 pages
Book Rating : 4.8/5 (714 download)

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Book Synopsis Geometry and Topology of Manifolds by : Hans U. Boden

Download or read book Geometry and Topology of Manifolds written by Hans U. Boden and published by American Mathematical Soc.. This book was released on with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains expository papers that give an up-to-date account of recent developments and open problems in the geometry and topology of manifolds, along with several research articles that present new results appearing in published form for the first time. The unifying theme is the problem of understanding manifolds in low dimensions, notably in dimensions three and four, and the techniques include algebraic topology, surgery theory, Donaldson and Seiberg-Witten gauge theory, Heegaard Floer homology, contact and symplectic geometry, and Gromov-Witten invariants. The articles collected for this volume were contributed by participants of the Conference "Geometry and Topology of Manifolds" held at McMaster University on May 14-18, 2004 and are representative of the many excellent talks delivered at the conference.

Geometric Topology

Author : James C. Cantrell
Publisher : Elsevier
ISBN 13 : 1483271315
Total Pages : 712 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Geometric Topology by : James C. Cantrell

Download or read book Geometric Topology written by James C. Cantrell and published by Elsevier. This book was released on 2014-05-10 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Topology contains the proceedings of the 1977 Georgia Topology Conference, held at the University of Georgia on August 1977. The book is comprised of contributions from leading experts in the field of geometric topology.These contributions are grouped into four sections: low dimensional manifolds, topology of manifolds, shape theory and infinite dimensional topology, and miscellaneous problems. Subjects discussed under these sections include local spanning missing loops, the structure of generalized manifolds having nonmanifold set of trivial dimension, universal open principal fibrations, and how to build a flexible polyhedral surface. Topologists, geometers, and mathematicians will find the book very interesting and insightful.

Surveys on Surgery Theory (AM-145), Volume 1

Author : Sylvain Cappell
Publisher : Princeton University Press
ISBN 13 : 1400865190
Total Pages : 448 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Surveys on Surgery Theory (AM-145), Volume 1 by : Sylvain Cappell

Download or read book Surveys on Surgery Theory (AM-145), Volume 1 written by Sylvain Cappell and published by Princeton University Press. This book was released on 2014-09-08 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. There have been some extraordinary accomplishments in that time, which have led to enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source that surveys surgery theory and its applications. Indeed, no one person could write such a survey. The sixtieth birthday of C. T. C. Wall, one of the leaders of the founding generation of surgery theory, provided an opportunity to rectify the situation and produce a comprehensive book on the subject. Experts have written state-of-the-art reports that will be of broad interest to all those interested in topology, not only graduate students and mathematicians, but mathematical physicists as well. Contributors include J. Milnor, S. Novikov, W. Browder, T. Lance, E. Brown, M. Kreck, J. Klein, M. Davis, J. Davis, I. Hambleton, L. Taylor, C. Stark, E. Pedersen, W. Mio, J. Levine, K. Orr, J. Roe, J. Milgram, and C. Thomas.

Approximation Results in Topological Manifolds

Author : Thomas A. Chapman
Publisher : American Mathematical Soc.
ISBN 13 : 0821822519
Total Pages : 64 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Approximation Results in Topological Manifolds by : Thomas A. Chapman

Download or read book Approximation Results in Topological Manifolds written by Thomas A. Chapman and published by American Mathematical Soc.. This book was released on 1981 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: A number of results are established concerning the approximation of maps between topological manifolds by homeomorphisms, approximate fibrations, and block bundles. Applications are given to the approximation of approximate fibrations by block bundles, and to the taming of locally homotopically unknotted embeddings.

Arbeitstagung Bonn 2013

Author : Werner Ballmann
Publisher : Birkhäuser
ISBN 13 : 3319436481
Total Pages : 425 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Arbeitstagung Bonn 2013 by : Werner Ballmann

Download or read book Arbeitstagung Bonn 2013 written by Werner Ballmann and published by Birkhäuser. This book was released on 2016-11-11 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected papers authored by speakers and participants of the 2013 Arbeitstagung, held at the Max Planck Institute for Mathematics in Bonn, Germany, from May 22-28. The 2013 meeting (and this resulting proceedings) was dedicated to the memory of Friedrich Hirzebruch, who passed away on May 27, 2012. Hirzebruch organized the first Arbeitstagung in 1957 with a unique concept that would become its most distinctive feature: the program was not determined beforehand by the organizers, but during the meeting by all participants in an open discussion. This ensured that the talks would be on the latest developments in mathematics and that many important results were presented at the conference for the first time. Written by leading mathematicians, the papers in this volume cover various topics from algebraic geometry, topology, analysis, operator theory, and representation theory and display the breadth and depth of pure mathematics that has always been characteristic of the Arbeitstagung.

The Geometry and Topology of Coxeter Groups. (LMS-32)

Author : Michael Davis
Publisher : Princeton University Press
ISBN 13 : 1400845947
Total Pages : 600 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis The Geometry and Topology of Coxeter Groups. (LMS-32) by : Michael Davis

Download or read book The Geometry and Topology of Coxeter Groups. (LMS-32) written by Michael Davis and published by Princeton University Press. This book was released on 2012-11-26 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures.