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Orientation-reversing involutions on handlebodies
Author(s):
John
Kalliongis;
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  -fibers of some  -bundle structure. As applications, various results of R. Nelson are proved without restrictive hypotheses.
References:
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- 2.
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- 8.
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 -manifolds, Invent. Math. 86 (1986), 287--346. MR 88b:57039 - 9.
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- 13.
- W. Thurston, The geometry and topology of 3-manifolds, mimeographed notes, Princeton University.
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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:
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
Copyright of article:
Copyright
1996,
American Mathematical Society
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