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Preprint Number 722

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722. Tomohiro Kawakami and Ikumitsu Nagasaki
A definable Borsuk-Ulam type theorem
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Submission date: 9 May 2014.


Let N=(R, +, . , <, ...) be an o-minimal expansion of the standard structure of a real closed field R. A definably compact definable group G is a definable Borsuk-Ulam group if there exists an isovariant definable map f:V \to W between representations of G, then dim V-dim V^G \leq \dim W-\dim W^G. We prove that if a finite group G satisfies the prime condition, then G is a definable Borsuk-Ulam group.

Mathematics Subject Classification: 57S10, 57S17, 55M35, 03C64.

Keywords and phrases: A definable Borsuk-Ulam type theorem, finite groups, o-minimal, real closed fields.

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