Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): 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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