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The Symmetries of Genus One Handlebodies

Published online by Cambridge University Press:  20 November 2018

John Kalliongis  and
Andy Miller
John Kalliongis
Affiliation:
Department of Mathematics St. Louis University St. Louis, MO 63103
Andy Miller
Affiliation:
Department of Mathematics University of Oklahoma Norman, OK 73019
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The symmetries of manifolds are a focal point of study in low-dimensional topology and yet, outside of some totally asymmetrical 3- and 4-manifolds, there are very few cases in which a complete classification has been attained. In this work we provide such a classification for symmetries of the orientable and nonorientable 3-dimensional handlebodies of genus one. Our classification includes a description, up to isomorphism, of all of the finite groups which can arise as symmetries on these manifolds, as well as an enumeration of the different ways in which they can arise. To be specific, we will classify the equivalence, weak equivalence and strong equivalence classes of (effective) finite group actions on the genus one handlebodies.

Keywords

57M9957S2557S30
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 2 , 01 April 1991 , pp. 371 - 404
Copyright
Copyright © Canadian Mathematical Society 1991

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