Topics in Topology and Homotopy Theory
Garth Warner
AMS Classification numbers: 55P, 55N, 55R, 55U
Department of Mathematics, Box 354350, University of Washington, Seattle, WA
98195-4350
warner@math.washington.edu
eps file "top-homotopy.eps" included
This book is a systematic account of the homotopical foundations of
algebraic topology. The depth of coverage is substantial and I have made a
point to include material which is ordinarily not included.
Here is a sample of what is taken up.
(1) Nilpotency and its role in homotopy theory.
(2) Bousfield's theory of the localization of spaces and spectra.
(3) Homotopy limits and colimits and their applications.
(4) The James construction, symmetric products, and the Dold-Thom theorem.
(5) Brown and Adams representability in the setting of triangulated
categories.
(6) Operads and the May-Thomason theorem on the uniqueness of infinite
loop space machines.
(7) The plus construction and theorems A and B of Quillen.
(8) Hopkins' global picture of stable homotopy theory.
(9) Model categories, cofibration categories, and Waldhausen categories.
(10) The Dugundji extension theorem and its consequences.