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Lifting homotopies through fixed points II

Published online by Cambridge University Press:  14 November 2011

M. A. Armstrong
M. A. Armstrong
Affiliation:
Department of Mathematical Sciences, University of Durham, Durham
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Synopsis

This note complements an earlier paper of the same title. Let G be a discontinuous group of homeomorphisms of a connected, locally path connected, Hausdorff space X, and let ∏:X → X/G denote the associated projection. We work relative to a G-invariant subgroup H of the fundamental group of X and investigate the quotient group ∏1(X/G)/∏*(H). By choosing H appropriately, we can calculate ∏1(X/G) and show that ∏1(X/G)/∏*(∏1(X)) is isomorphic to G/F, where F is the normal subgroup of G generated by those elements which have fixed points. In a final section, we give analogous results for actions of a compact Lie group.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 3-4 , 1984 , pp. 201 - 205
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Armstrong, M. A.. Lifting homotopies through fixed points. Proc. Roy. Soc. Edinburgh Sect. A 93 (1982), 123–128.CrossRefGoogle Scholar
2Armstrong, M. A.. Calculating the fundamental group of an orbit space. Proc. Amer. Math. Soc. 84 (1982), 267–271.CrossRefGoogle Scholar
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4Spanier, E. H.. Algebraic Topology (New York: McGraw-Hill, 1966).Google Scholar