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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$\textrm {PL}$ involutions on lens spaces and other $3$-manifolds
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by Paik Kee Kim
Proc. Amer. Math. Soc. 44 (1974), 467-473
DOI: https://doi.org/10.1090/S0002-9939-1974-0375363-0

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 ${P^3}\# {P^3}$.
References
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Bibliographic Information
  • © Copyright 1974 American Mathematical Society
  • 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