Abstract
In this chapter we shall prove some quite deep results about the homotopy groups of CW-complexes and relative CW-complexes. Most of these hard theorems will be consequences of the simplicial approximation theorem. In addition, we shall show that if f: X → Y is a map between CW-complexes such that f*: π n (X, x0) → π n (Y, y0) is an isomorphism for all n ⩾ 0, then f is a homotopy equivalence.
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References
E. Dyer [37]
P. J. Hilton and S. Wylie [45]
E. H. Spanier [80]
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© 2002 Springer-Verlag Berlin Heidelberg
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Switzer, R.M. (2002). Homotopy Properties of CW-Complexes. In: Algebraic Topology — Homotopy and Homology. Classics in Mathematics, vol 212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61923-6_7
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DOI: https://doi.org/10.1007/978-3-642-61923-6_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42750-6
Online ISBN: 978-3-642-61923-6
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