Transactions of the American Mathematical Society

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

 

 

$ {\rm PL}$ involutions of $ S\sp{1}\times S\sp{1}\times S\sp{1}$


Authors: Kyung Whan Kwun and Jeffrey L. Tollefson
Journal: Trans. Amer. Math. Soc. 203 (1975), 97-106
MSC: Primary 57E25
MathSciNet review: 0370634
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0370634-1
Article copyright: © Copyright 1975 American Mathematical Society