Differential topology / Gereon Quick

Format:

Book

Author/Creator:

Quick, Gereon, author.

Series:

London Mathematical Society student texts ; 113.

London Mathematical Society student texts ; 113

Language:

English

Subjects (All):

Differential topology.

Differential topology--Problems, exercises, etc.

Genre:

Problems and exercises

Physical Description:

1 online resource

Place of Publication:

Cambridge : Cambridge University Press, 2026

Summary:

"Differential topology uncovers the hidden structure of smooth spaces –the foundation of modern geometry and topology. This book offers a clear, rigorous introduction to the subject, blending theory with concrete examples and applications. Beginning with the basics of manifolds and smooth maps, it develops essential tools and concepts such as tangent spaces, transversality, cobordism, and tubular neighbourhoods, before progressing to powerful invariants like the Brouwer degree, intersection numbers, and the Hopf invariant. Along the way, readers encounter landmark results including Whitney's embedding theorem, Brouwer's fixed point theorem, the Pontryagin construction, Hopf's degree theorem, and the Poincaré–Hopf index theorem. Each chapter combines intuitive explanations with precise and detailed proofs, supported by exercises and detailed solutions that deepen understanding. Ideal for advanced undergraduates, graduate students, and researchers, this text provides a gateway to one of mathematics' most elegant and influential fields – where analysis, geometry, and topology meet"-- Cambridge Core

Contents:

A brief introduction to topological spaces

Smooth manifolds

The inverse function theorem, immersions, and embeddings

Submersions and regular values

Transversality

Abstract smooth manifolds

Whitney’s embedding theorems

Smooth homotopy

Manifolds with boundary

Brouwer fixed point theorem

The Brouwer degree modulo 2

Tubular neighbourhoods and transversality

Intersection theory modulo 2

Orientation

The integer-valued Brouwer degree

Pontryagin construction and Hopf’s degree theorem

Vector fields and the Poincaré–Hopf index theorem

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (Cambridge Core, viewed August 21, 2026)

Other Format:

Print version: Quick, Gereon Differential topology

ISBN:

9781009759861

1009759868

9781009759847

1009759841

OCLC:

1578773108

Publisher Number:

CIPO000415794

Access Restriction:

Restricted for use by site license