A combinatorial introduction to topology
Book Description
Excellent text for upper-level undergraduate and graduate students shows how geometric and algebraic ideas met and grew together into an important branch of mathematics. Lucid coverage of vector fields, surfaces, homology of complexes, much more. Some knowledge of differential equations and multivariate calculus required. Many problems and exercises (some solutions) integrated into the text. 1979 edition. Bibliography.
Table Of Content
Chapter One Basic Concepts
1 The Combinatorial Method
2 Continuous Transformations in the Plane
3 Compactness and Connectedness
4 Abstract Point Set Topology
Chapter Two Vector Fields
5 A Link Between Analysis and Topology
6 Sperner's Lemma and the Brouwer Fixed Point Theorem
7 Phase Portraits and the Index Lemma
8 Winding Numbers
9 Isolated Critical Points
10 The Poincaré Index Theorem
11 Closed Integral Paths
12 Further Results and Applications
Chapter Three Plane Homology and Jordan Curve Theorem
13 Polygonal Chains
14 The Algebra of Chains on a Grating
15 The Boundary Operator