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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Homotopy groups of the isotropy groups of annulus


Author: Jong P. Lee
Journal: Proc. Amer. Math. Soc. 44 (1974), 213-217
MSC: Primary 57E05; Secondary 55E05
DOI: https://doi.org/10.1090/S0002-9939-1974-0328965-1
MathSciNet review: 0328965
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Abstract: We compute the isotopy groups of various subspaces of the isotropy group at an interior point of an annulus. We also prove that if $ a$ and $ x$ are interior points of a disk $ D$, then $ {\pi _0}[H(D - a,x)] = {Z_2}$ and $ {\pi _n}[H(D - a,x)] = 0$ for $ n \geqq 1$ where $ H(D - a,x)$ is the isotropy group at $ x$.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0328965-1
Keywords: Homeomorphism, homotopy group, isotopy group, isotropy group, winding number, homeotopy exact sequence
Article copyright: © Copyright 1974 American Mathematical Society