Imbeddings of free actions on handlebodies

McCullough, Darryl

doi:10.1090/S0002-9939-02-06754-0

Imbeddings of free actions on handlebodies
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Proc. Amer. Math. Soc. 131 (2003), 2247-2253 Request permission

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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