Book Review: Homotopy theory; an introduction to algebraic topology

Abstract

Preliminaries -- Some simple topological spaces -- Some simple topological problems --Homotopy theory -- Category theory -- The fundamental group --More on the fundamental group --Calculating the fundamental group --A convenient category of topological spaces -- Track groups and homotopy groups -- Relative homotopy groups -- Locally trivial bundles -- Simplicial complexes and linearity -- Calculating homotopy groups : the Blakers-Massey theorem -- The topology of CW complexes -- Limits -- The homotopy theory of CW complexes -- K(π, n)'s and Postnikov systems -- Spectral reduced homology and cohomology theories -- Spectral unreduced homology and cohomology theories -- Ordinary homology of CW complexes -- Homology and cohomology groups of more general spaces -- The relation between homotopy and ordinary homology -- Multivariate structure -- Relations between chain complexes -- Homological algebra over a principal ideal domain (Künneth and universal coefficient theorems -- Orientation and duality -- Cohomology operations -- Adem relations -- K-Theories -- Cobordism.