Homotopy Theory

  • Edwin H. Spanier


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.


Homotopy Class Homotopy Type Homotopy Group Free Homotopy Class Weak Homotopy 
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Copyright information

© Springer-Verlag New York, Inc. 1966

Authors and Affiliations

  • Edwin H. Spanier
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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