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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Orientation-reversing involutions on handlebodies


Authors: John Kalliongis and Darryl McCullough
Journal: Trans. Amer. Math. Soc. 348 (1996), 1739-1755
MSC (1991): Primary 57M60; Secondary 57S25
MathSciNet review: 1329535
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Abstract: The observation that the quotient orbifold of an orientation- reversing involution on a 3-dimensional handlebody has the structure of a compression body leads to a strong classification theorem, and general structure theorems. The structure theorems decompose the action along invariant discs into actions on handlebodies which preserve the $I$-fibers of some $I$-bundle structure. As applications, various results of R. Nelson are proved without restrictive hypotheses.


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Additional Information

John Kalliongis
Affiliation: Department of Mathematics, St. Louis University, St. Louis, Missouri 63103
Email: kalliongisje@sluvca.slu.edu

Darryl McCullough
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
Email: dmccullough@uoknor.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01515-2
PII: S 0002-9947(96)01515-2
Keywords: 3-manifold, orbifold, handlebody, orientation-reversing, group action, involution, $I$-bundle, fiber-preserving, compression body, classification
Received by editor(s): June 29, 1994
Received by editor(s) in revised form: May 4, 1995
Article copyright: © Copyright 1996 American Mathematical Society