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Imbeddings of free actions on handlebodies

Author: Darryl McCullough
Journal: Proc. Amer. Math. Soc. 131 (2003), 2247-2253
MSC (2000): Primary 57M60; Secondary 57M50
Published electronically: October 15, 2002
MathSciNet review: 1963774
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Abstract: Fix a free, orientation-preserving action of a finite group $G$ on a $3$-dimensional handlebody $V$. Whenever $G$ acts freely preserving orientation on a connected $3$-manifold $X$, there is a $G$-equivariant imbedding of $V$ into $X$. There are choices of $X$ closed and Seifert-fibered for which the image of $V$ is a handlebody of a Heegaard splitting of $X$. Provided that the genus of $V$ is at least $2$, there are similar choices with $X$ closed and hyperbolic.

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Additional Information

Darryl McCullough
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019

Keywords: 3-manifold, handlebody, group action, free, free action, imbed, imbedding, equivariant, invariant, hyperbolic, Seifert, Heegaard, Heegaard splitting, Whitehead link
Received by editor(s): October 9, 2001
Received by editor(s) in revised form: February 14, 2002
Published electronically: October 15, 2002
Additional Notes: The author was supported in part by NSF grant DMS-0102463
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2002 American Mathematical Society