International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1990 / Article

Open Access

Volume 13 |Article ID 518547 | https://doi.org/10.1155/S0161171290000059

Roger B. Nelson, "A decomposition into homeomorphic handlebodies with naturally equivalent involutions", International Journal of Mathematics and Mathematical Sciences, vol. 13, Article ID 518547, 6 pages, 1990. https://doi.org/10.1155/S0161171290000059

A decomposition into homeomorphic handlebodies with naturally equivalent involutions

Abstract

Downing [6] extended the well-known result that any closed 3-manifold X contains a handlebody H such that c1(XH) is homeomorphic to H in the case where X is a compact 3-manifold with nonvoid boundary. We show that if X is a compact 3-manifold with involution h having 2-dimensional fixed point set, then X contains an h-invariant handlebody H such that the involutions induced on H and c1(XH) are naturally equivalent.

Copyright © 1990 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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