Homotopy and Homology Decompositions

Abstract

In this chapter we discuss methods of approximating a space by simpler spaces. We assign to a space X a sequence of spaces whose nth term is called the nth section of X. As n gets larger, the nth section of X becomes a better approximation to X. There are two basic techniques for this, one in terms of the homotopy groups of X, called the homotopy decomposition, and the other in terms of the homology groups of X, called the homology decomposition.