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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Equivalence and strong equivalence of actions on handlebodies


Authors: John Kalliongis and Andy Miller
Journal: Trans. Amer. Math. Soc. 308 (1988), 721-745
MSC: Primary 57S25; Secondary 57M12, 57M15
DOI: https://doi.org/10.1090/S0002-9947-1988-0951625-5
MathSciNet review: 951625
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Abstract: An algebraic characterization is given for the equivalence and strong equivalence classes of finite group actions on $ 3$-dimensional handlebodies. As one application it is shown that each handlebody whose genus is bigger than one admits only finitely many finite group actions up to equivalence. In another direction, the algebraic characterization is used as a basis for deriving an explicit combinatorial description of the equivalence and strong equivalence classes of the cyclic group actions of prime order on handlebodies with genus larger than one. This combinatorial description is used to give a complete closed-formula enumeration of the prime order cyclic group actions on such handlebodies.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0951625-5
Keywords: Handlebody, finite group action, handlebody orbifold, graph of groups, equivalence and strong equivalence of actions
Article copyright: © Copyright 1988 American Mathematical Society