Descuento:
-5%Antes:
Despues:
76,95 €Basic Definitions 14
Chapter 1. Graphs18
1. Topological and Geometric Properties of Graphs18
2. Homotopy Properties of Graphs42
3. Graph Invariants60
Chapter 2. Topology in Euclidean Space68
1. Topology of Subsets of Euclidean Space68
2. Curves in the Plane76
3. The Brouwer Fixed Point Theorem and Sperner's Lemma85
Chapter 3. Topological Spaces100
1. Elements of General Topology100
2. Simplicial Complexes112
3. CW-Complexes130
4. Constructions143
Chapter 4. Two-Dimensional Surfaces, Coverings, Bundles, and Homotopy Groups152
1. Two-Dimensional Surfaces152
2. Coverings162
3. Graphs on Surfaces and Deleted Products of Graphs170
4. Fibrations and Homotopy Groups174
Chapter 5. Manifolds194
1. Definition and Basic Properties194
2. Tangent Spaces212
3. Embeddings and Immersions220
4. The Degree of a Map233
5. Morse Theory252
Chapter 6. Fundamental Groups270
1. CW-Complexes270
2. The Seifert-van Kampen Theorem279
3. Fundamental Groups of Complements of Algebraic Curves292
Hints and Solutions304
Bibliography
Modern topology uses very diverse methods. This book is devoted largely to methods of combinatorial topology, which reduce the study of topological spaces to investigations of their partitions into elementary sets, and to methods of differential topology, which deal with smooth manifolds and smooth maps. Many topological problems can be solved by using either of these two kinds of methods, combinatorial or differential. In such cases, both approaches are discussed.
One of the main goals of this book is to advance as far as possible in the study of the properties of topological spaces (especially manifolds) without employing complicated techniques. This distinguishes it from the majority of other books on topology.
The book contains many problems; almost all of them are supplied with hints or complete solutions.
-5%
-5%
-5%
-5%
-5%
-5%
-5%
-5%
-5%
-5%
-5%
