Fixed point sets of homeomorphisms of metric products

Author:
John R. Martin

Journal:
Proc. Amer. Math. Soc. **103** (1988), 1293-1298

MSC:
Primary 55M20; Secondary 54H25, 57M25, 57N99

DOI:
https://doi.org/10.1090/S0002-9939-1988-0955025-9

MathSciNet review:
955025

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper it is investigated as to when a nonempty closed subset of a metric product containing intervals or spheres as factors can be the fixed point set of an autohomeomorphism of . It is shown that if is the Hilbert cube or contains either the real line or a -sphere as a factor, then can be any nonempty closed subset. In the case where is in , the interior of the closed unit , a strong necessary condition is given. In particular, for can neither be a nonamphicheiral knot nor a standard closed or nonplanar bordered surface.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0955025-9

Keywords:
Fixed point set,
orientation preserving (reversing) autohomeomorphism,
Hilbert cube,
knot,
closed surface,
bordered surface

Article copyright:
© Copyright 1988
American Mathematical Society