Large groups of symmetries of handlebodies

Authors:
A. Miller and B. Zimmermann

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

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Abstract: Let be an orientable three-dimensional handlebody with genus . Let be the largest order among all finite groups which act effectively on and preserve orientation. We show that , and that equals either or when is odd. Moreover each of the indicated upper and lower bounds are achieved for infinitely many genera . 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0962246-9

Keywords:
-dimensional handlebody,
finite group action,
graph of groups,
compact -manifold with boundary

Article copyright:
© Copyright 1989
American Mathematical Society