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An index theory for $\mathbb{Z}$-actions

Author: In-Sook Kim
Journal: Proc. Amer. Math. Soc. 126 (1998), 2481-2491
MSC (1991): Primary 58G10, 58F27, 34D20, 58E40; Secondary 34C35
MathSciNet review: 1459129
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Abstract: This paper concerns an index theory for $\Bbb Z$-actions induced by a homeomorphism of a compact space. We give a definition of a genus for uniform spaces and prove that the genus for compact spaces is an index. To this end we show a ${\Bbb Z}$-version of the Borsuk-Ulam theorem and the existence of a continuous equivariant extension for these $\Bbb Z$-actions.

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Additional Information

In-Sook Kim
Affiliation: Department of Mathematics, Sung Kyun Kwan University, Suwon 440-746, Korea

Keywords: Index, genus, almost periodic, Lyapunov stable, group actions
Received by editor(s): January 22, 1997
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 1998 American Mathematical Society