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Incompressible surfaces in the exterior of a closed 3-braid

I. Surfaces with horizontal boundary components

Published online by Cambridge University Press:  24 October 2008

María Teresa Lozano  and
Józef H. Przytycki
María Teresa Lozano
Affiliation:
Facultad de Ciencias, Universidad de Zaragoza, Spain
Józef H. Przytycki
Affiliation:
Department of Mathematics, University of Warsaw, Poland
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Extract

Let be a closed 3-braid in S3 with axis Lγ. The exterior of γ U Lγ in S3 is a fibre bundle over S1 with fibre a disc with 3 holes. The monodromy is given by a matrix in PSL(2,) and the braid γ is called hyperbolic if its matrix is hyperbolic.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 2 , September 1985 , pp. 275 - 299
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Bleiler, S. A.. Knots prime on many strings (University of Texas at Austin, 1982). (Preprint.)Google Scholar
[2]Floyd, W. and Hatcher, A.. Incompressible surfaces in punctured-torus bundles. Topology Appl. 13 (1982), 263–282.CrossRefGoogle Scholar
[3]Floyd, W. and Hatcher, A.. Incompressible surfaces in 2-bridge link complements (Preprint).Google Scholar
[4]Gross, J. L.. A unique decomposition theorem for 3-manifolds with connected boundary. Trans. Amer. Math. Soc. 142 (1969), 191–199.CrossRefGoogle Scholar
[5]Gross, J. L.. The decomposition of 3-manifolds with several boundary components. Trans. Amer. Mat. Soc. 147 (1970), 561–572.Google Scholar
[6]Hatcher, A. and Thurston, W.. Incompressible surfaces in 2-bridge knot complements (Preprint).Google Scholar
[7]Hempel, J.. Constructions of orientable 3-manifolds. Topology of 3-manifolds and related topics, ed. Fort, M. K. (1961), pp. 207–212.Google Scholar
[8]Jaco, W.. Addinga 2-handle to a 3-manifold: An application to Property R (Preprint, 1982).Google Scholar
[9]Lickobish, W. B. R.. Prime knots and tangles. Trans. Amer. Math. Soc. 267 (1981), 321–332.CrossRefGoogle Scholar
[10]Lozano, M. T.. Arcbodies. Math. Proc. Cambridge Philos. Soc. 94 (1983), 253–260.CrossRefGoogle Scholar
[11]Lyon, G. H.. Incompressible surfaces in the boundary of a handlebody - an algorithm. Canad. J. Math. 32 (1980), 590–595.CrossRefGoogle Scholar
[12]Menasco, W.. Closed incompressible surfaces in alternating knot and link complements. Topology 23 (1984), 37–44.CrossRefGoogle Scholar
[13]Murasugi, K.. On closed 3-braids (Memoirs Amer. Math. Soc, vol. 151, 1974).Google Scholar
[14]Pbzytycki, J. H.. Incompressibility of surfaces after Dehn surgery. Michigan Math. J. (To appear.)Google Scholar
[15]Pbzytycki, J. H.. Nonorientable, incompressible surfaces in punctured-torus bundles over S2. Pacific J. Math. (To appear.)Google Scholar
[16]Przytycki, J. H.. Incompressible surfaces, class of March 9 (1983) xeroxed notes.Google Scholar
[17]THubston, W.. The geometry and topology of 3-manifolds (Princeton University Press) (To appear).Google Scholar
[18]Waldhausen, F.. Eine Klasse von 3-dimensionalen Mannigfaltigkeiten I. Invent. Math. 3 (1967), 308–333 and II. Invent. Math. 4 (1967), 87–117.Google Scholar