Applications Of The H Cobordism Theorem

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Applications Of The H Cobordism Theorem

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Author : Matthew Bryan Burkemper
language : en
Publisher:
Release Date : 2014

Applications Of The H Cobordism Theorem written by Matthew Bryan Burkemper and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Electronic dissertations categories.

We provide an exposition of J. Milnor's proof of the h-Cobordism Theorem. This theorem states that a smooth, compact, simply connected n-dimensional manifold W with n greater than or equal to 6, whose boundary boundaryW consists of a pair of closed simply connected (n-1)-dimensional manifolds M0 and M1 and whose relative integral homology groups H(W,M0) are all trivial, is diffeomorphic to the cylinder M0 x [0, 1]. The proof makes heavy use of Morse Theory and in particular the cancellation of certain pairs of Morse critical points of a smooth function. We pay special attention to this cancellation and provide some explicit examples. An important application of this theorem concerns the generalized Poincare conjecture, which states that a closed simply connected n-dimensional manifold with the integral homology of the n-dimensional sphere is homeomorphic to the sphere. We discuss the proof of this conjecture in dimension n greater than or equal to 6, which is a consequence of the h-Cobordism Theorem.

Lectures On The H Cobordism Theorem

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Author : John Milnor
language : en
Publisher: Princeton University Press
Release Date : 2025-03-25

Lectures On The H Cobordism Theorem written by John Milnor and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-25 with Mathematics categories.

Important lectures on differential topology by acclaimed mathematician John Milnor These are notes from lectures that John Milnor delivered as a seminar on differential topology in 1963 at Princeton University. These lectures give a new proof of the h-cobordism theorem that is different from the original proof presented by Stephen Smale. Milnor's goal was to provide a fully rigorous proof in terms of Morse functions. This book remains an important resource in the application of Morse theory.

Selected Applications Of Geometry To Low Dimensional Topology

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Author : Michael H. Freedman
language : en
Publisher: American Mathematical Soc.
Release Date : 1990

Selected Applications Of Geometry To Low Dimensional Topology written by Michael H. Freedman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.

Based on lectures presented at Pennsylvania State University in February 1987, this work begins with the notions of manifold and smooth structures and the Gauss-Bonnet theorem, and proceeds to the topology and geometry of foliated 3-manifolds. It also explains why four-dimensional space has special attributes.

Algebraic K Theory And Its Applications

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Author : Jonathan Rosenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Algebraic K Theory And Its Applications written by Jonathan Rosenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the fall of 1990, is intended to enable graduate students or mathematicians working in other areas not only to learn the basics of algebraic K-Theory, but also to get a feel for its many applications. The required prerequisites are only the standard one-year graduate algebra course and the standard introductory graduate course on algebraic and geometric topology. Many topics from algebraic topology, homological algebra, and algebraic number theory are developed as needed. The final chapter gives a concise introduction to cyclic homology and its interrelationship with K-Theory.

Controlled Simple Homotopy Theory And Applications

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Author : T. A. Chapman
language : en
Publisher: Springer
Release Date : 2006-11-14

Controlled Simple Homotopy Theory And Applications written by T. A. Chapman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Essays In Mathematics And Its Applications

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Author : Panos M. Pardalos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-07

Essays In Mathematics And Its Applications written by Panos M. Pardalos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-07 with Mathematics categories.

​The volume is dedicated to Stephen Smale on the occasion of his 80th birthday.Besides his startling 1960 result of the proof of the Poincar ́e conjecture for all dimensionsgreater than or equal to five, Smale’s ground breaking contributions invarious fields in Mathematics have marked the second part of the 20th century andbeyond. Stephen Smale has done pioneering work in differential topology, globalanalysis, dynamical systems, nonlinear functional analysis, numerical analysis, theoryof computation and machine learning as well as applications in the physical andbiological sciences and economics. In sum, Stephen Smale has manifestly brokenthe barriers among the different fields of mathematics and dispelled some remainingprejudices. He is indeed a universal mathematician. Smale has been honoredwith several prizes and honorary degrees including, among others, the Fields Medal(1966), The Veblen Prize (1966), the National Medal of Science (1996) and theWolfPrize (2006/2007).

Collected Papers Of Stephen Smale The In 3 Volumes Volume 1

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Author : Roderick S C Wong
language : en
Publisher: World Scientific
Release Date : 2000-06-30

Collected Papers Of Stephen Smale The In 3 Volumes Volume 1 written by Roderick S C Wong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-30 with Mathematics categories.

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 Collected Papers Of Stephen Smale

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Author : Stephen Smale
language : en
Publisher: World Scientific
Release Date : 2000

The Collected Papers Of Stephen Smale written by Stephen Smale and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

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.

Critical Point Theory In Global Analysis And Differential Topology

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Author :
language : en
Publisher: Academic Press
Release Date : 2014-05-14

Critical Point Theory In Global Analysis And Differential Topology written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Mathematics categories.

Critical Point Theory in Global Analysis and Differential Topology

Differential And Low Dimensional Topology

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Author : András Juhász
language : en
Publisher: Cambridge University Press
Release Date : 2023-04-20

Differential And Low Dimensional Topology written by András Juhász and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-20 with Mathematics categories.

A concise introduction to the most important parts of differential and low-dimensional topology for incoming graduate students.