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$ {\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
DOI: https://doi.org/10.1090/S0002-9939-1974-0375363-0
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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0375363-0
Keywords: PL involution, invariant set, fixed point set, lens space
Article copyright: © Copyright 1974 American Mathematical Society

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