Involutions on and other manifolds
Author:
Jeffrey L. Tollefson
Journal:
Trans. Amer. Math. Soc. 183 (1973), 139152
MSC:
Primary 57A10; Secondary 55A10
MathSciNet review:
0326738
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Abstract: This paper exploits the following observation concerning involutions on nonreducible 3manifolds: If the dimension of the fixed point set of a PL involution is less than or equal to one then there exists a pair of disjoint 2spheres that do not bound 3cells and whose union is invariant under the given involution. The classification of all PL involutions of is obtained. In particular, admits exactly thirteen distinct PL involutions (up to conjugation). It follows that there is a unique PL involution of the solid torus with 1dimensional fixed point set. Furthermore, there are just four fixed point free actions and just one fixed point free action on for each positive integer k (again, up to conjugation). The above observation is also used to obtain a general description of compact, irreducible 3manifolds that admit twosided embeddings of the projective plane.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197303267380
PII:
S 00029947(1973)03267380
Keywords:
Threemanifolds,
involution,
cyclic group action
Article copyright:
© Copyright 1973
American Mathematical Society
