Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T14:25:47.149Z Has data issue: false hasContentIssue false

Dehn fillings of Klein bottle bundles

Published online by Cambridge University Press:  24 October 2008

Wolfgang Heil
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306–3027, U.S.A.
Pedja Raspopović
Affiliation:
Department of Mathematics, University of Titograd, 81000 Titograd, Yugoslavia

Extract

An important problem in the topology of 3-manifolds is to classify manifolds obtained by Dehn surgeries on a knot in a closed 3-manifold, or equivalently, Dehn fillings of a 3-manifold M with boundary a torus.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Baker, M.. Covers of Dehn fillings on once-punctured torus bundles. Preprint.Google Scholar
[2]Culler, M., Jaco, W., and Rubinstein, H.. Incompressible surfaces in once-punctured torus bundles. Proc. London Math. Soc. (3) 45 (1982), 385419.CrossRefGoogle Scholar
[3]Floyd, W. and Hatcher, A.. Incompressible surfaces in punctured torus bundles. Topology Appl. 13 (1982), 263282.CrossRefGoogle Scholar
[4]McGordon, C. and Luecke, J.. Knots are determined by their complements. Bull. Amer. Math. Soc. 20 (1989), 8387.Google Scholar
[5]Hatcher, A. E.. On the boundary curves of incompressible surfaces. Pacific J. Math. 99 (1982), 373377.CrossRefGoogle Scholar
[6]Hatcher, A. E.. Notes on basic 3-manifold topology. (Preprint).Google Scholar
[7]Hatcher, A. E. and Thurston, W.. Incompressible surfaces in 2-bridge knot complements. Invent. Math. 79 (1985), 225246.CrossRefGoogle Scholar
[8]Heil, W.. On certain fiberings of M2 × S1. Proc. Amer. Math. Soc. 34 (1972), 280286.Google Scholar
[9]Hempel, J.. 3-manifolds. Ann. of Math. Studies no. 86 (Princeton University Press, 1976).Google Scholar
[10]Jaco, W.. Lectures on 3-manifold topology. Regional Conf. Series in Math. no. 43 (1980).CrossRefGoogle Scholar
[11]Jaco, W.. Surfaces embedded in M2 × S1. Canad. J. Math. 22 (1970), 553568.CrossRefGoogle Scholar
[12]Lickorish, W. B. R.. Homeomorphisms of non-orientable two-manifolds. Proc. Cambridge Philos. Soc. 59 (1963), 307317.CrossRefGoogle Scholar
[13]Neumann, D. A.. 3-manifolds fibering over S1. Proc. Amer. Math. Soc. 58 (1976), 353356.Google Scholar
[14]Orlik, P., Vogt, E. and Zieschang, H.. Zur Topologie gefaserter 3-dimensionaler Mannigfaltigkeiten. Topology 6 (1967), 4964.CrossRefGoogle Scholar
[15]Raspopović, P.. Incompressible surfaces in punctured Klein bottle bundles. Preprint.Google Scholar
[16]Raspopović, P.. Incompressible surfaces in punctured Klein bottle bundles. Ph.D. thesis, Florida State University (1990).Google Scholar
[17]Scott, P.. The geometries of 3-manifolds. Bull. London Math. Soc. 15 (1983), 401487.CrossRefGoogle Scholar
[18]Seifert, H.. Über die Topologie 3-dimensionaler gefaserter Räume. Ada Math. 60 (1933), 147288. English translation inGoogle Scholar
A Textbook of Topology (Academic Press, 1980), pp. 358422.Google Scholar
[19]Soma, T.. Equivariant surfaces in 3-manifolds with abelian group actions. Bull. Kyushu Inst. Tech. Math. Natur. Sci. 36 (1989), 19.Google Scholar
[20]Stallings, J.. On fibering certain 3 manifolds. In Topology of 3-Manifolds and Related Topics (Prentice Hall, 1962), pp. 95100.Google Scholar
[21]Steenrod, N.. The Topology of Fibre Bundles (Princeton University Press, 1951).Google Scholar
[22]Thurston, W.. The Geometry and Topology of 3-manifolds. Lecture Notes, Princeton University (1979).Google Scholar
[23]Tollefson, J.. 3-manifolds fiberings over S1 with nonunique connected fiber. Proc. Amer. Math. Soc. 21 (1969), 7980.Google Scholar
[24]Waldhausen, F.. Eine Klasse von 3-dimensionaler. Mannigfaltkeiten II. Invent. Math. 4 (1967), 87117.CrossRefGoogle Scholar