Max Karoubi, C. Leruste

Algebraic Topology Via Differential Geometry

• Broschiertes Buch

Produktbeschreibung

In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry.

Table of contents:
Introduction; 1. Algebraic preliminaries; 2. differential forms on an open subset of Rn; 3. differentiable manifolds; 4. De Rham cohomology of differentiable manifolds; 5. Computing cohomology; 6. Poincaré duality - Lefschetz' theorem; Appendixes; Bibliography; Index.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 376
• Erscheinungstermin: 1. Januar 1987
• Englisch
• Abmessung: 229mm x 152mm x 22mm
• Gewicht: 609g
• ISBN-13: 9780521317146
• ISBN-10: 0521317142
• Artikelnr.: 20984089

Inhaltsangabe

Introduction
1. Algebraic preliminaries
2. differential forms on an open subset of Rn
3. differentiable manifolds
4. De Rham cohomology of differentiable manifolds
5. Computing cohomology
6. Poincaré duality - Lefschetz' theorem
Appendixes
Bibliography
Index.