Lefschetz's Topology was written in the period in between the beginning of topology, by Poincare, and the establishment of algebraic topology as a well-formed subject, separate from point-set or geometric topology. At this time, Lefschetz had already proved his first fixed-point theorems. In some sense, the present book is a description of the broad subject of topology into which Lefschetz's theory of fixed points fits. Lefschetz takes the opportunity to describe some of the important applications of his theory, particularly in algebraic geometry, to problems such as counting intersections of algebraic varieties. He also gives applications to vector distributions, complex spaces, and Kronecker's characteristic theory.
Elementary combinatorial theory of complexes Topological invariance of the homology characters Manifolds and their duality theorems Intersections of chains on a manifold Product complexes Transformations of manifolds, their coincidences and fixed points Infinite complexes and their applications Applications to analytical and algebraic varieties Bibliography Addenda Index.