involutions of some -manifolds

Author:
Myung Mi Myung

Journal:
Proc. Amer. Math. Soc. **33** (1972), 576-581

MSC:
Primary 57C99; Secondary 55C35, 57E30

DOI:
https://doi.org/10.1090/S0002-9939-1972-0295363-7

MathSciNet review:
0295363

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Abstract | References | Similar Articles | Additional Information

Abstract: Let and be PL involutions of connected, oriented, closed, irreducible 3-manifolds and , respectively. Let , be a fixed point of such that near the fixed point sets of are of the same dimension. Then we obtain a PL involution on induced by by taking the connected sum of and along neighborhoods of . In this paper, we study the possibility for a PL involution *h* on having a 2-dimensional fixed point set to be of the form , where are lens spaces. It is shown that: (1) if is orientable, then and *h* is the obvious involution, (2) if the fixed point set *F* contains a projective plane, then projective 3-space, and in this case, *F* is the disjoint union of two projective planes and *h* is unique up to PL equivalences, (3) if *F* contains a Klein bottle *K*, then *F* is the disjoint union of a Klein bottle and two points.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0295363-7

Keywords:
PL involution,
lens space,
connected sum

Article copyright:
© Copyright 1972
American Mathematical Society