Topology and Geometry

This book is intended as a textbook for a first-year graduate course on algebraic topology, with as strong flavoring in smooth manifold theory. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. It covers most of the topics all topologists will want students to see, including surfaces, Lie groups and fibre bundle theory.

Klappentext

This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory.

From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."--MATHEMATICAL REVIEWS

Zusammenfassung
From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."--MATHEMATICAL REVIEWS

Inhalt
I General Topology.- II Differentiable Manifolds.- III Fundamental Group.- IV Homology Theory.- V Cohomology.- VI Products and Duality.- VII Homotopy Theory.- Appendices.- App. A. The Additivity Axiom.- App. B. Background in Set Theory.- App. C. Critical Values.- App. D. Direct Limits.- App. E. Euclidean Neighborhood Retracts.- Index of Symbols.