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Imbeddings of free actions on handlebodies
Authors:Darryl McCullough
Affiliation:Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
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.

Keywords:3-manifold   handlebody   group action   free   free action   imbed   imbedding   equivariant   invariant   hyperbolic   Seifert   Heegaard   Heegaard splitting   Whitehead link
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