Customer Reviews

Foundations of Combinatorial Topology

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This book covers, as the title says, the foundations of combinatorial topology. What that refers to, essentially, is the topology of polyhedra and the machinery of simplicial homology groups. The first part of the book establishes the basic facts about these topological spaces and about abstract complexes as well. The second part shows the topological invariance of simplicial homology. The third features applications of the material to fixed point theory.

Throughout the book there is also a recurring digression on dimension theory, which culminates in a proof of the very non-trivial fact that manifolds have the appropriate topological dimension.

The only formal pre-requisites for this book are basic linear algebra and point-set topology, as covered in any advanced calculus or elementary real analysis course.

The presentation is very concise and lucid throughout. I can imagine some people not liking such an extremely concise style, but the whole book is so logical that it works very well.

proofs are very detailed almost pedagogic. the author always points out the goal first then digs in. the only flaw is its visual presentation - rather condensed type set. i think Pontryagin was a truly educational teacher. good for self study.