Foundations of Combinatorial Topology

by L.S. Pontryagin

This concise but very rigorous introduction to homology theory is based on a series of lectures delivered by the author at Moscow National University and translated from the first (1947) Russian edition. Focusing on application to dimension theory and fixed-point theorems, the text lucidy exanines complexes and their Betti Groups (including Euclidean space, application to dimension theory and decomposition into components), invariance of the Betti groups, with consideration given to the cone construction and barycentric subdivisions of a complex; and continuous mapping and fixed points. Proofs are presented in a complete, careful, and elegant manner.

Hardcover

First published February 9, 1999

About the author

Lev Semyonovich Pontryagin (Russian: Лев Семёнович Понтря́гин) was a Soviet mathematician.