Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A unique decomposition of involutions of handlebodies

Author: Roger B. Nelson
Journal: Proc. Amer. Math. Soc. 93 (1985), 358-362
MSC: Primary 57S25; Secondary 57Q99, 57S17
MathSciNet review: 770554
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Abstract: We consider a PL involution of an orientable, $ 3$-dimensional handlebody for which each component of the fixed point set is $ 2$-dimensional. The handlebody is uniquely equivariantly decomposed as a disk sum of handlebodies $ {M_i}$ such that if $ {M_i} \approx {A_i} \times I$, then $ h\vert{M_i}$ is equivalent to (i) $ \alpha \times {\text{i}}{{\text{d}}_I}$, where $ \alpha $ is an involution of $ A$, or to (ii) $ {\text{i}}{{\text{d}}_a} \times r$, where $ r(t) = - t$ for all $ t \in I = [ - 1,1]$.

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Keywords: Involution, equivalent involutions, equivariant decompositions of handlebodies, $ 2$-dimensional fixed point set, invariant properly embedded disks
Article copyright: © Copyright 1985 American Mathematical Society