Large groups of symmetries of handlebodies

Miller, A.; Zimmermann, B.

doi:10.1090/S0002-9939-1989-0962246-9

Large groups of symmetries of handlebodies
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by A. Miller and B. Zimmermann PDF

Proc. Amer. Math. Soc. 106 (1989), 829-838 Request permission

Abstract:

Let ${V_g}$ be an orientable three-dimensional handlebody with genus $g > 1$. Let $N(g)$ be the largest order among all finite groups which act effectively on ${V_g}$ and preserve orientation. We show that $4(g + 1) \leq N(g) \leq 12(g - 1)$, and that $N(g)$ equals either $8(q - 1)$ or $12(g - 1)$ when $g$ is odd. Moreover each of the indicated upper and lower bounds are achieved for infinitely many genera $g$. The techniques which are used lead to more detailed results and also specialize to yield similar results for compact surfaces with nonempty boundary.

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