𝑃𝐿 involutions on lens spaces and other 3-manifolds

Kim, Paik Kee

doi:10.1090/S0002-9939-1974-0375363-0

$\textrm {PL}$ involutions on lens spaces and other $3$-manifolds
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Proc. Amer. Math. Soc. 44 (1974), 467-473 Request permission

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 ${P^3}\# {P^3}$.

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