Foundational Essays On Topological Manifolds Smoothings And Triangulations

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

Robion C. Kirby,Laurence C. Siebenmann
Foundational Essays on Topological Manifolds Smoothings and Triangulations AM 88 Volume 88 Book PDF

Author : Robion C. Kirby,Laurence C. Siebenmann
Publisher : Princeton University Press
Page : 368 pages
File Size : 54,7 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881505

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Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88 by Robion C. Kirby,Laurence C. Siebenmann Pdf

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 Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.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

Robion C. Kirby,Laurence Carl Siebenmann
Foundational Essays on Topological Manifolds Smoothings and Triangulations Book PDF

Author : Robion C. Kirby,Laurence Carl Siebenmann
Publisher : Annals of Mathematics Studies
Page : 355 pages
File Size : 51,8 Mb
Release : 1977
Category : Mathematics
ISBN : 0691081905

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Foundational Essays on Topological Manifolds, Smoothings, and Triangulations by Robion C. Kirby,Laurence Carl Siebenmann Pdf

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

Morris W. Hirsch,Jerrold E. Marsden,Michael Shub
From Topology to Computation Proceedings of the Smalefest Book PDF

Author : Morris W. Hirsch,Jerrold E. Marsden,Michael Shub
Publisher : Springer Science & Business Media
Page : 620 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461227403

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From Topology to Computation: Proceedings of the Smalefest by Morris W. Hirsch,Jerrold E. Marsden,Michael Shub Pdf

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.

Piecewise Linear Structures on Topological Manifolds

Yuli RUDYAK
Piecewise Linear Structures on Topological Manifolds Book PDF

Author : Yuli RUDYAK
Publisher : World Scientific
Page : 129 pages
File Size : 52,9 Mb
Release : 2015-12-28
Category : Mathematics
ISBN : 9789814733793

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Piecewise Linear Structures on Topological Manifolds by Yuli RUDYAK Pdf

"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

Stefan Behrens,Boldizsar Kalmar,Min Hoon Kim,Mark Powell,Arunima Ray
The Disc Embedding Theorem Book PDF

Author : Stefan Behrens,Boldizsar Kalmar,Min Hoon Kim,Mark Powell,Arunima Ray
Publisher : Oxford University Press
Page : 300 pages
File Size : 55,5 Mb
Release : 2021-07-15
Category : Mathematics
ISBN : 9780192578389

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The Disc Embedding Theorem by Stefan Behrens,Boldizsar Kalmar,Min Hoon Kim,Mark Powell,Arunima Ray Pdf

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

F Cucker,R Wong
The Collected Papers of Stephen Smale Book PDF

Author : F Cucker,R Wong
Publisher : World Scientific
Page : 1740 pages
File Size : 50,6 Mb
Release : 2000-06-30
Category : Mathematics
ISBN : 9789814493055

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The Collected Papers of Stephen Smale by F Cucker,R Wong Pdf

'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

Stephen Smale,Felipe Cucker,Roderick Wong
The Collected Papers of Stephen Smale Book PDF

Author : Stephen Smale,Felipe Cucker,Roderick Wong
Publisher : World Scientific
Page : 532 pages
File Size : 45,9 Mb
Release : 2000
Category : Mathematics
ISBN : 9810249918

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The Collected Papers of Stephen Smale by Stephen Smale,Felipe Cucker,Roderick Wong Pdf

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.

The Wild World of 4-Manifolds

Alexandru Scorpan
The Wild World of 4 Manifolds Book PDF

Author : Alexandru Scorpan
Publisher : American Mathematical Society
Page : 614 pages
File Size : 53,7 Mb
Release : 2022-01-26
Category : Mathematics
ISBN : 9781470468613

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The Wild World of 4-Manifolds by Alexandru Scorpan Pdf

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.

Geometric Topology

James C. Cantrell
Geometric Topology Book PDF

Author : James C. Cantrell
Publisher : Elsevier
Page : 712 pages
File Size : 46,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483271316

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Geometric Topology by James C. Cantrell Pdf

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.

Surgery on Compact Manifolds

Charles Terence Clegg Wall,Andrew Ranicki
Surgery on Compact Manifolds Book PDF

Author : Charles Terence Clegg Wall,Andrew Ranicki
Publisher : American Mathematical Soc.
Page : 321 pages
File Size : 41,7 Mb
Release : 1999
Category : Manifolds (Mathematics).
ISBN : 9780821809426

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Surgery on Compact Manifolds by Charles Terence Clegg Wall,Andrew Ranicki Pdf

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.

Approximation Results in Topological Manifolds

Thomas A. Chapman
Approximation Results in Topological Manifolds Book PDF

Author : Thomas A. Chapman
Publisher : American Mathematical Soc.
Page : 64 pages
File Size : 55,8 Mb
Release : 1981
Category : Mathematics
ISBN : 9780821822517

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Approximation Results in Topological Manifolds by Thomas A. Chapman Pdf

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.

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

Francesco Lin
A Morse Bott Approach to Monopole Floer Homology and the Triangulation Conjecture Book PDF

Author : Francesco Lin
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 53,6 Mb
Release : 2018-10-03
Category : Floer homology
ISBN : 9781470429638

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

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.

Arbeitstagung Bonn 2013

Werner Ballmann,Christian Blohmann,Gerd Faltings,Peter Teichner,Don Zagier
Arbeitstagung Bonn 2013 Book PDF

Author : Werner Ballmann,Christian Blohmann,Gerd Faltings,Peter Teichner,Don Zagier
Publisher : Birkhäuser
Page : 425 pages
File Size : 41,7 Mb
Release : 2016-11-11
Category : Mathematics
ISBN : 9783319436487

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Arbeitstagung Bonn 2013 by Werner Ballmann,Christian Blohmann,Gerd Faltings,Peter Teichner,Don Zagier Pdf

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.

Algebraic and Geometric Topology

R. James Milgram
Algebraic and Geometric Topology Book PDF

Author : R. James Milgram
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 48,8 Mb
Release : 1978
Category : Mathematics
ISBN : 9780821814338

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Algebraic and Geometric Topology by R. James Milgram Pdf

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.

The Topological Classification of Stratified Spaces

Shmuel Weinberger
The Topological Classification of Stratified Spaces Book PDF

Author : Shmuel Weinberger
Publisher : University of Chicago Press
Page : 314 pages
File Size : 41,6 Mb
Release : 1994
Category : Mathematics
ISBN : 0226885666

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The Topological Classification of Stratified Spaces by Shmuel Weinberger Pdf

This book provides the theory for stratified spaces, along with important examples and applications, that is analogous to the surgery theory for manifolds. In the first expository account of this field, Weinberger provides topologists with a new way of looking at the classification theory of singular spaces with his original results. Divided into three parts, the book begins with an overview of modern high-dimensional manifold theory. Rather than including complete proofs of all theorems, Weinberger demonstrates key constructions, gives convenient formulations, and shows the usefulness of the technology. Part II offers the parallel theory for stratified spaces. Here, the topological category is most completely developed using the methods of "controlled topology." Many examples illustrating the topological invariance and noninvariance of obstructions and characteristic classes are provided. Applications for embeddings and immersions of manifolds, for the geometry of group actions, for algebraic varieties, and for rigidity theorems are found in Part III. This volume will be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry.