Topics in Topology and Homotopy Theory

Abstract

This book is addressed to those readers who have been through Rotman (or its equivalent), possess a wellthumbed copy of Spanier, and have a good background in algebra and general topology.

Granted these prerequisites, my intention is to provide at the core a state of the art treatment of the homotopical foundations of algebraic topology. The depth of coverate is substantial and I have made a point to include material which is ordinarily not included, for instance, an account of algebraic K-theory in the sense of Waldhausen. There is also a systematic treatment of ANR theory (but, reluctantly, the connections with modern geometric topology have been omitted). However, truly advanced topics are not considered (e.g., equivalent stable homotopy theory, surgery, infinite dimensional topology, étale K-theory, ...). Still, one should not get the impression that what remains is easy: There are numerous difficult technical results that have to be brought to heel.