Elements of Combinatorial and Differential Topology (Graduate Studies in Mathematics, Vol. 74)

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.--book Jacket. Basic Definitions Chapter 1. Graphs Chapter 2. Topology In Euclidean Space Chapter 3. Topological Spaces Chapter 4. Two-dimensional Surfaces, Coverings, Bundles, And Homotopy Groups Chapter 5. Manifolds Chapter 6. Fundamental Groups Hints And Solutions V.v. Prasolov ; [translated From The Russian By Olga Sipacheva]. Includes Bibliographical References (p. 317-323) And Index. Translated From The Russian. Cover......Page 0 Copyright page......Page 3 Contents......Page 4 1 Graphs......Page 16 2 Topology in Euclidean space......Page 66 3 Topological spaces......Page 97 4 Two-dimensional surfaces, coverings, bundles and homotopy groups......Page 148 5 Manifolds......Page 190 6 Fundamental groups......Page 266 Hints and solutions......Page 300 Bibliography......Page 326 Index......Page 333 Many topological problems can be solved by using either combinatorial or differential methods. The main goal of this text is to advance as far as possible in the study of the properties of topological spaces (especially manifolds) without employing complicated techniques Cover 1 Copyright page 3 Contents 4 1 Graphs 16 2 Topology in Euclidean space 66 3 Topological spaces 97 4 Two-dimensional surfaces, coverings, bundles and homotopy groups 148 5 Manifolds 190 6 Fundamental groups 266 Hints and solutions 300 Bibliography 326 Index 333