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This Book is in Good Condition. Clean Copy With Light Amount of Wear. 100% Guaranteed. Summary: 1: Two-Dimensional Manifolds. 2: The Fundamental Group. 3: Free Groups and Free Products of Groups. 4: Seifert and Van Kampen Theorem on the Fundamental Group of the Union of Two Spaces. Applications. 5: Covering Spaces. 6: Background and Motivation for Homology Theory. 7: Definitions and Basic Properties of Homology Theory. 8: Determination of the Homology Groups of Certain Spaces: Applications and Further Properties of Homology Theory. 9: Homology of CW-Complexes. 10: Homology with Arbitrary Coefficient Groups. 11: The Homology of Product Spaces. 12: Cohomology Theory. 13: Products in Homology and Cohomology. 14: Duality Theorems for the Homology of Manifolds. 15: Cup Products in Projective Spaces and Applications of Cup Products. Appendix A: A Proof of De Rham's Theorem. Appendix B: Permutation Groups or Tranformation Groups. Bookseller Inventory #

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Synopsis: The main purpose of this book is to give a systematic treatment of singular homology and cohomology theory. It is in some sense a sequel to the author's previous book in this Springer-Verlag series entitled Algebraic Topology: An Introduction. This earlier book is definitely not a logical prerequisite for the present volume. However, it would certainly be advantageous for a prospective reader to have an acquaintance with some of the topics treated in that earlier volume, such as 2-dimensional manifolds and the funda­ mental group. Singular homology and cohomology theory has been the subject of a number of textbooks in the last couple of decades, so the basic outline of the theory is fairly well established. Therefore, from the point of view of the mathematics involved, there can be little that is new or original in a book such as this. On the other hand, there is still room for a great deal of variety and originality in the details of the exposition. In this volume the author has tried to give a straightforward treatment of the subject matter, stripped of all unnecessary definitions, terminology, and technical machinery. He has also tried, wherever feasible, to emphasize the geometric motivation behind the various concepts.

Review: W.S. Massey

A Basic Course in Algebraic Topology

"In the minds of many people algebraic topology is a subject which is esoteric, specialized, and disjoint from the overall sweep of mathematical thought. This straightforward introduction to the subject, by a recognized authority, aims to dispel that point of view by emphasizing: 1. the geometric motivation for the various concepts and 2. the applications to other areas."BULLETIN OF THE IRISH MATHEMATICS SOCIETY

W.S. Massey

A Basic Course in Algebraic Topology

"In the minds of many people algebraic topology is a subject which is a ~esoteric, specialized, and disjoint from the overall sweep of mathematical thought.a (TM) This straightforward introduction to the subject, by a recognized authority, aims to dispel that point of view by emphasizing: 1. the geometric motivation for the various concepts and 2. the applications to other areas."a "BULLETIN OF THE IRISH MATHEMATICS SOCIETY

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