𝑃𝐿 involutions of 𝑆¹×𝑆¹×𝑆¹

Kwun, Kyung Whan; Tollefson, Jeffrey L.

doi:10.1090/S0002-9947-1975-0370634-1

$\textrm {PL}$ involutions of $S^{1}\times S^{1}\times S^{1}$
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by Kyung Whan Kwun and Jeffrey L. Tollefson

Trans. Amer. Math. Soc. 203 (1975), 97-106

DOI: https://doi.org/10.1090/S0002-9947-1975-0370634-1

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Abstract:

We prove that the $3$-dimensional torus ${S^1} \times {S^1} \times {S^1}$ admits exactly nine nonequivalent PL involutions. With the exception of the four fixed point free ones, the involutions may be distinguished by their fixed point sets: (1) eight points, (2) two simple closed curves, (3) four simple closed curves, (4) one torus, (5) two tori.

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