Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-26T03:05:41.454Z Has data issue: false hasContentIssue false

On Homeomorphisms of a 3-Dimensional Handlebody

Published online by Cambridge University Press:  20 November 2018

Shin'ichi Suzuki*
Affiliation:
University of Toronto, Toronto, Ontario
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

By a 3-dimensional handlebody Vn of genus n, we mean an oriented 3-manifold which is a disk-sum of n copies of D2 X S1, where D2 is the unit disk and S1 is the boundary ∂D2; and by a surface Fn of genus n we mean the oriented boundary surface ∂ Vn.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Baer, R., Isotopie von Kurven auf orientierbaren, geschlossenen Fldchen und ihr Zusammenhang mit der topologischen Deformation der Fldchen, J. reine angew. Math., 159 (1928), 101- 111.Google Scholar
2. Birman, J. S., On Siegel's modular group, Math. Ann. 191 (1971), 5968.Google Scholar
3. Birman, J. S. Mapping class groups 0﹜ surfaces: A survey, Ann. of Math. Studies 79, Discontinuous Groups and Riemann Surfaces, ed. Greenberg (Princeton Univ. Press, Princeton, N.J., 1974), 5771.Google Scholar
4. Birman, J. S. Braids, links and mapping class groups, Ann. of Math. Studies 82 (Princeton Univ. Press, Princeton N.J., 1974).Google Scholar
5. Birman, J. S. Poincaré conjecture and the homeotopy group of a closed orientable 2-manifold, J. Aust. Math. Soc. 17 (1974), 214221.Google Scholar
6. Birman, J. S. and Hilden, H. M., On the mapping class groups of closed surfaces as covering spaces , Ann. of Math. Studies 66, Advances on the Theory of Riemann Surfaces, ed. Ahlfors et al. (Princeton Univ. Press, Princeton, N.J., 1972), 81115.Google Scholar
7. Dehn, M., Die Gruppe der Abbildungsklassen, Acta Math. 69 (1938), 135206.Google Scholar
8. Epstein, D. B. A., Curves on 2-manifolds and isotopies, Acta Math. 115 (1966), 83107.Google Scholar
9. Goeritz, L., Die Abbildungen der Brezelflachen und der Vollbrezel vom Geschlecht 2, Abh. Math. Sem. Univ. Hamburg, 9 (1933), 244259.Google Scholar
10. Griffiths, H. B., Automorphisms of a 3-dimensional handlebody, Abh. Math. Sem. Univ. Hamburg 26 (1964), 191210.Google Scholar
11. Griffiths, H. B. Some elementary topology of 3-dimensional handlebodies, Comm. Pure and Appl. Math. 17 (1964), 317334.Google Scholar
12. Hua, L. K. and Reiner, I., On the generators of the symplectic modular group, Trans. Amer. Math. Soc. 65 (1949), 415426.Google Scholar
13. Klingen, H., Charakterisierung der Siegelschen Modulgruppe durch ein endliches System definierender Relationen, Math. Ann. 144 (1901), 6482.Google Scholar
14. Lickorish, W. B. R., A finite set of generators for the homeotopy group of a 2-manifold, Proc. Camb. Phil. Soc. 60 (1964), 769-778. Also Corrigendum, 62 (1966), 679681.Google Scholar
15. Mangier, W., Die klassen von topologischen Abbildungen einer geschlossenen Flache auf sich, Math. Z. U(1939), 541554.10.1007/978-3-662-41389-0_1CrossRefGoogle Scholar
16. Nielsen, J., Untersuchen zur Topologie der geschlossenen Zweiseitigen Flàchen I, Acta Math. 50 (1927), 184-358. Also, Acta Math. 58 (1932), 87167.Google Scholar