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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Calculating the fundamental group of an orbit space


Author: M. A. Armstrong
Journal: Proc. Amer. Math. Soc. 84 (1982), 267-271
MSC: Primary 55Q05; Secondary 57S99
MathSciNet review: 637181
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Abstract: Suppose $ G$ acts effectively as a group of homeomorphisms of the connected, locally path connected, simply connected, locally compact metric space $ X$. Let $ \overline G $ denote the closure of $ G$ in $ {\text{Homeo}}(X)$, and $ N$ the smallest normal subgroup of $ \overline G $ which contains the path component of the identity of $ \overline G $ and all those elements of $ \overline G $ which have fixed points. We show that $ {\pi _1}(X/G)$ is isomorphic to $ \overline G /N$ subject to a weak path lifting assumption for the projection $ X \to X/\overline G $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0637181-X
PII: S 0002-9939(1982)0637181-X
Article copyright: © Copyright 1982 American Mathematical Society