An index theory for ℤ-actions

Kim, In-Sook

doi:10.1090/S0002-9939-98-04451-7

An index theory for $\mathbb Z$-actions
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by In-Sook Kim PDF

Proc. Amer. Math. Soc. 126 (1998), 2481-2491 Request permission

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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