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Homeomorphisms of the 3-sphere that preserve a Heegaard splitting of genus two
Author(s):
Sangbum
Cho
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1113-1123.
MSC (2000):
Primary 57M40
Posted:
November 30, 2007
MathSciNet review:
2361888
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Abstract:
Let  be the group of isotopy classes of orientation-preserving homeomorphisms of  that preserve a Heegaard splitting of genus two. In this paper, we construct a tree in the barycentric subdivision of the disk complex of a handlebody of the splitting to obtain a finite presentation of  .
References:
-
- 1.
- E. Akbas, A presentation for the automorphisms of the 3-sphere that preserve a genus two Heegaard splitting, preprint, 2005, ArXiv:math.GT/0504519.
- 2.
- L. Goeritz, Die Abbildungen der Berzelfläche und der Volbrezel vom Gesschlect 2, Abh. Math. Sem. Univ. Hamburg 9 (1933), 244-259.
- 3.
- C. McA. Gordon, On primitive sets of loops in the boundary of a handlebody, Topology Appl. 27 (1987), no. 3, 285-299. MR 918538 (88k:57013)
- 4.
- S. Hirose, Homeomorphisms of a 3-dimensional handlebody standardly embedded in
 , KNOTS '96 (Tokyo), World Sci. Publ, River Edge, NJ (1997), 493-513. MR 1664983 (99k:57037) - 5.
- D. McCullough, Virtually geometrically finite mapping class groups of 3-manifolds, J. Differential Geom. 33, (1991), no. 1, 1-65. MR 1085134 (92c:57001)
- 6.
- J. Powell, Homeomorphisms of
 leaving a Heegaard surface invariant, Trans. Amer. Math. Soc. 257 (1980), no. 1, 193-216. MR 549161 (80m:57005) - 7.
- M. Scharlemann, Automorphisms of the 3-sphere that preserve a genus two Heegaard splitting, Bol. Soc. Mat. Mexicana (3) 10 (2004), Special Issue, 503-514. MR 2199366 (2007c:57020)
- 8.
- J. Serre, Trees, Springer-Verlag, 1980. ix+142 pp. MR 607504 (82c:20083)
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Additional Information:
Sangbum
Cho
Affiliation:
Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
Email:
scho@math.ou.edu
DOI:
10.1090/S0002-9939-07-09188-5
PII:
S 0002-9939(07)09188-5
Received by editor(s):
November 6, 2006
Posted:
November 30, 2007
Communicated by:
Daniel Ruberman
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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