Large groups of symmetries of handlebodies
Authors:
A. Miller and B. Zimmermann
Journal:
Proc. Amer. Math. Soc. 106 (1989), 829838
MSC:
Primary 57M99; Secondary 57S25, 57S30
MathSciNet review:
962246
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Abstract: Let be an orientable threedimensional 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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 N. Greenleaf and C. May, Bordered Klein surfaces with maximal symmetry, Trans. Amer. Math. Soc. 274 (1982), 265283. MR 670931 (84f:14022)
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 W. J. Harvey, Cyclic groups of automorphisms of a compact Riemann surface, Quart. J. Math. Oxford Ser. (2) 17 (1966), 8697. MR 0201629 (34:1511)
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 C. Maclachlan, A bound for the number of automorphisms of a compact Riemann surface, J. London Math. Soc. 44 (1969), 265272. MR 0236378 (38:4674)
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 C. May, A bound for the number of automorphisms of a compact Klein surface with boundary, Proc. Amer. Math. Soc. 63 (1977), 273280. MR 0435385 (55:8345)
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 , Uber Homoömorphismen dimensionaler Henkelkörper und endliche Erweiterungen von SchottkyGruppen, Comment. Math. Helv. 56 (1981), 474486. MR 639363 (83f:57025)
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 , Classification of groups of automorphisms of Riemann surfaces and their lower central series, Glasgow Math. J. 29 (1987), 237244. MR 901670 (88j:20050)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198909622469
PII:
S 00029939(1989)09622469
Keywords:
dimensional handlebody,
finite group action,
graph of groups,
compact manifold with boundary
Article copyright:
© Copyright 1989
American Mathematical Society
