Homotopy Theory

Edwin H. Spanier
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Edwin H. Spanier: University of California, Department of Mathematics

Chapter Chapter Seven in Algebraic Topology, 1966, pp 362-421 from Springer

Abstract: Abstract with this chapter we return to the consideration of general homotopy theory. Now that we have homology theory available as a tool, we are able to obtain deeper results about homotopy than we could without it. We shall consider the higher homotopy groups in some detail and prove they satisfy analogues of all the axioms of homology theory except the excision axiom. We introduce the Hurewicz homomorphism as a natural transformation from the homotopy groups to the integral singular homology groups. It leads us to the Hurewicz isomorphism theorem, which states roughly that the lowest-dimensional nontrivial homotopy group is isomorphic to the corresponding integral homology group.

Keywords: Homotopy Class; Homotopy Type; Homotopy Group; Free Homotopy Class; Weak Homotopy (search for similar items in EconPapers)
Date: 1966
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DOI: 10.1007/978-1-4684-9322-1_8

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