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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



$ {\rm PL}$ involutions on lens spaces and other $ 3$-manifolds

Author: Paik Kee Kim
Journal: Proc. Amer. Math. Soc. 44 (1974), 467-473
MSC: Primary 57E25
MathSciNet review: 0375363
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Abstract: Let $ h$ be an involution of a $ 3$-dimensional lens space $ L = L(p,q)$. $ h$ is called sense preserving if $ h$ induces the identity of $ {H_1}(L)$. The purpose of this paper is to classify the orientation preserving PL involutions of $ L$ which preserve sense and have nonempty fixed point sets for $ p$ even. It follows that, up to PL equivalences, there are exactly three PL involutions on the projective $ 3$-space $ {P^3}$, and exactly seven PL involutions on $ {P^3}\char93 {P^3}$.

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Keywords: PL involution, invariant set, fixed point set, lens space
Article copyright: © Copyright 1974 American Mathematical Society