-PDF Download- Foundational Essays On Topological Manifolds Smoothings And Triangulations EBOOK

Foundational Essays on Topological Manifolds, Smoothings, and Triangulations

Author: Robion C. Kirby

Publisher: Princeton University Press

Published: 1977-05-21

Total Pages: 376

ISBN-13: 9780691081915

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 Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.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. (AM-88), Volume 88

Author: Robion C. Kirby

Publisher: Princeton University Press

Published: 2016-03-02

Total Pages: 368

ISBN-13: 1400881501

DOWNLOAD EBOOK →

From Topology to Computation: Proceedings of the Smalefest

Author: Morris W. Hirsch

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 620

ISBN-13: 1461227402

DOWNLOAD EBOOK →

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

Published: 2022-01-26

Total Pages: 614

ISBN-13: 1470468611

DOWNLOAD EBOOK →

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

Published: 2015-12-28

Total Pages: 129

ISBN-13: 9814733792

DOWNLOAD EBOOK →

"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

Published: 2021-07-15

Total Pages: 300

ISBN-13: 0192578383

DOWNLOAD EBOOK →

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

Published: 2000-06-30

Total Pages: 1740

ISBN-13: 9814493058

DOWNLOAD EBOOK →

'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'

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

Author: Francesco Lin

Publisher: American Mathematical Soc.

Published: 2018-10-03

Total Pages: 162

ISBN-13: 1470429632

DOWNLOAD EBOOK →

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.

Algebraic and Geometric Topology, Part 2

Author: R. James Milgram

Publisher: American Mathematical Soc.

Published: 1978

Total Pages: 330

ISBN-13: 0821814338

DOWNLOAD EBOOK →

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.

Geometry and Topology of Manifolds

Author: Hans U. Boden

Publisher: American Mathematical Soc.

Published:

Total Pages: 368

ISBN-13: 9780821871492

DOWNLOAD EBOOK →

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.