Topics in differential topology [electronic resource] / Amiya Mukherjee.

Call Number	514.72
Author	Mukherjee, Amiya.
Title	Topics in differential topology Amiya Mukherjee.
Edition	1st ed.
Physical Description	1 online resource (459 pages)
Series	Texts and Readings in Mathematics ; 34
Contents	Topics in differential topology -- Preface -- Contents -- Chapter 1: Basic Concepts of Manifolds -- Chapter 2: Approximation Theorems and Whitney's Embedding -- Chapter 3: Linear Structures on Manifolds -- Chapter 4: Riemannian Manifolds -- Chapter 5: Vector Bundles on Manifolds -- Chapter 6: Transversality -- Chapter 7: Tubular Neighbourhoods -- Chapter 8: Spaces of Smooth Maps -- Chapter 9: Morse Theory -- Chapter 10: Theory of Handle Presentations -- Chapter 11: Homotopy Classificaytion of Regular Sections -- Bibliography -- Index -- Texts and Readings in Mathematics.
Summary	Aimed at those who have an elementary knowledge of linear algebra, general topology, multivariate calculus, analysis, and algebraic topology, this book gives an introduction to some fundamental tools of differential topology. The first part, comprising chapters 1 to 4, is foundational. It will be useful to general students of pure mathematics and can be used to design a course at the M.Sc. level in Indian universities. The second part, consisting of chapters 5 to 8, caters to researchers in the areas of topology, differential or algebraic geometry and global analysis, and touches on advanced topics of general interest in these areas. Finally, the third part is meant for those who want to work in the field of differential topology itself. Some of the highlights of the book are Thom transversality, Morse theory, Theory of handle presentation, h-cobordism theorem and generalized Poincaré conjecture, and Gromov theory of homotopy principle of certain partial differential relations. The intention is to acquaint the reader with some epochal discoveries in the field of manifolds, mainly the earlier works of Stephen Smale for which he was awarded the Fields Medal.
Subject	MATHEMATICS / General. Electronic books.
Multimedia	https://portal.igpublish.com/iglibrary/search/HBAB0000015.html

Total Ratings: 0

Copies
MARC Record
Reviews
Details


No records found to display.

03029nam a2200409 i 4500

001

vtls001596288

003

VRT

005

20220902105700.0

006

m eo d

007

cr cn |||m|||a

008

220902s2005 ob 000 0 eng d

020

$a 8185931569

020

$a 9788185931562

035

$a HBAB0000015

039

$y 202209021057 $z santha

041

$a eng

050

$a QA613.6

082

$a 514.72

100

$a Mukherjee, Amiya.

245

$a Topics in differential topology $h [electronic resource] / $c Amiya Mukherjee.

250

$a 1st ed.

264

$a New Delhi, Inde : $b Hindustan Book Agency, $c 2005.

264

300

$a 1 online resource (459 pages)

336

$a text $b txt $2 rdacontent

337

$a computer $b c $2 rdamedia

338

$a online resource $b cr $2 rdacarrier

490

$a Texts and Readings in Mathematics ; $v 34

504

$a Includes bibliographical references and index.

505

$a Topics in differential topology -- Preface -- Contents -- Chapter 1: Basic Concepts of Manifolds -- Chapter 2: Approximation Theorems and Whitney's Embedding -- Chapter 3: Linear Structures on Manifolds -- Chapter 4: Riemannian Manifolds -- Chapter 5: Vector Bundles on Manifolds -- Chapter 6: Transversality -- Chapter 7: Tubular Neighbourhoods -- Chapter 8: Spaces of Smooth Maps -- Chapter 9: Morse Theory -- Chapter 10: Theory of Handle Presentations -- Chapter 11: Homotopy Classificaytion of Regular Sections -- Bibliography -- Index -- Texts and Readings in Mathematics.

506

$a Access restricted to authorized users and institutions.

520

$a Aimed at those who have an elementary knowledge of linear algebra, general topology, multivariate calculus, analysis, and algebraic topology, this book gives an introduction to some fundamental tools of differential topology. The first part, comprising chapters 1 to 4, is foundational. It will be useful to general students of pure mathematics and can be used to design a course at the M.Sc. level in Indian universities. The second part, consisting of chapters 5 to 8, caters to researchers in the areas of topology, differential or algebraic geometry and global analysis, and touches on advanced topics of general interest in these areas. Finally, the third part is meant for those who want to work in the field of differential topology itself. Some of the highlights of the book are Thom transversality, Morse theory, Theory of handle presentation, h-cobordism theorem and generalized Poincaré conjecture, and Gromov theory of homotopy principle of certain partial differential relations. The intention is to acquaint the reader with some epochal discoveries in the field of manifolds, mainly the earlier works of Stephen Smale for which he was awarded the Fields Medal.

538

$a Mode of access: World Wide Web.

650

$a MATHEMATICS / General. $2 bisacsh

655

$a Electronic books.

856

$u https://portal.igpublish.com/iglibrary/search/HBAB0000015.html

999

$a VIRTUA

No Reviews to Display

Summary	Aimed at those who have an elementary knowledge of linear algebra, general topology, multivariate calculus, analysis, and algebraic topology, this book gives an introduction to some fundamental tools of differential topology. The first part, comprising chapters 1 to 4, is foundational. It will be useful to general students of pure mathematics and can be used to design a course at the M.Sc. level in Indian universities. The second part, consisting of chapters 5 to 8, caters to researchers in the areas of topology, differential or algebraic geometry and global analysis, and touches on advanced topics of general interest in these areas. Finally, the third part is meant for those who want to work in the field of differential topology itself. Some of the highlights of the book are Thom transversality, Morse theory, Theory of handle presentation, h-cobordism theorem and generalized Poincaré conjecture, and Gromov theory of homotopy principle of certain partial differential relations. The intention is to acquaint the reader with some epochal discoveries in the field of manifolds, mainly the earlier works of Stephen Smale for which he was awarded the Fields Medal.
Contents	Topics in differential topology -- Preface -- Contents -- Chapter 1: Basic Concepts of Manifolds -- Chapter 2: Approximation Theorems and Whitney's Embedding -- Chapter 3: Linear Structures on Manifolds -- Chapter 4: Riemannian Manifolds -- Chapter 5: Vector Bundles on Manifolds -- Chapter 6: Transversality -- Chapter 7: Tubular Neighbourhoods -- Chapter 8: Spaces of Smooth Maps -- Chapter 9: Morse Theory -- Chapter 10: Theory of Handle Presentations -- Chapter 11: Homotopy Classificaytion of Regular Sections -- Bibliography -- Index -- Texts and Readings in Mathematics.
Subject	MATHEMATICS / General. Electronic books.
Multimedia	https://portal.igpublish.com/iglibrary/search/HBAB0000015.html