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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

PL involutions of fibered $ 3$-manifolds


Authors: Paik Kee Kim and Jeffrey L. Tollefson
Journal: Trans. Amer. Math. Soc. 232 (1977), 221-237
MSC: Primary 57A10; Secondary 55C35
MathSciNet review: 0454981
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Abstract: Let h be a PL involution of $ F \times [0,1]$ such that $ h(F \times \{ 0,1\} ) = F \times \{ 0,1\} $, where F is a compact 2-manifold. It is shown that h is equivalent to an involution $ h'$ of the form $ h'(x,t) = (g(x),\lambda (t))$. This result is applied to classify the PL involutions of closed, orientable, Seifert manifolds when the fixed-point set contains a two-dimensional component of negative characteristic.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0454981-2
PII: S 0002-9947(1977)0454981-2
Keywords: Involutions, 3-manifolds
Article copyright: © Copyright 1977 American Mathematical Society