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.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 829-838
- MSC: Primary 57M99; Secondary 57S25, 57S30
- DOI: https://doi.org/10.1090/S0002-9939-1989-0962246-9
- MathSciNet review: 962246