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Homeomorphisms on the Solid Double Torus

Published online by Cambridge University Press:  20 November 2018

Donald Myers
Donald Myers*
Affiliation:
11837 Diane Drive, Wauwatosa, Wisconsin
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A finite set of generators for the isotopy classes of selfhomeomorphisms of closed surfaces was given by Lickorish in three papers [2; 3; 4]. In [5] the group of isotopy classes for a particular, well-known cube with holes was presented. There the structure was “tight” enough to allow the computation of the relators as well as the generators. In this paper we give a finite set of generators for the group of isotopy classes of self-homeomorphisms on the solid double torus, the cube with two handles. Let us remark that the group of isotopy classes for the solid torus is well-known.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 4 , 01 August 1975 , pp. 797 - 804
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Hudson, J. F. P., Piecewise linear topology (W. A. Benjamin, Inc., New York, 1969).Google Scholar
2. Lickorish, W. B. R., A representation of orientable combinatorial 3-manifolds, Ann. of Math. 76 (1962), 531–540.Google Scholar
3. Lickorish, W. B. R., Homeomorphisms of non-orientable two-manifolds, Proc. Cambridge Philos. Soc. 59 (1963), 307–317.Google Scholar
4. Lickorish, W. B. R., A finite set of generators for the homeotopy group of a 2-manifold, Proc. Cambridge Philos. Soc. 60 (1964), 769–778.Google Scholar
5. Myers, Donald, Homeomorphisms on a certain cube with holes, Trans. Amer. Math. Soc. 191 (1974), 289–299.Google Scholar