Singular Homology Theory

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 authors 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.