Abstract
In this chapter we shall demonstrate some of the elementary properties of the homotopy groups. Then we shall construct the relative homotopy groups π n (X, A, x0) of a pointed topological pair x0 ∈ A ⊂ X and show how they fit into a long exact sequence with the groups π n (A, x0) and π n (X, x0). Finally we shall discuss the relation between the groups π n (X, x0) and π n (X, x1) for different base points.
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References
P. J. Hilton [42]
H. Hopf [47]
S.-T. Hu [48]
E. H. Spanier [80]
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© 2002 Springer-Verlag Berlin Heidelberg
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Switzer, R.M. (2002). Properties of the Homotopy Groups. In: Algebraic Topology — Homotopy and Homology. Classics in Mathematics, vol 212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61923-6_4
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DOI: https://doi.org/10.1007/978-3-642-61923-6_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42750-6
Online ISBN: 978-3-642-61923-6
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