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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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$\textrm {PL}$ 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

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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Bibliographic Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 203 (1975), 97-106
  • MSC: Primary 57E25
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0370634-1
  • MathSciNet review: 0370634