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Constructions of arcbodies

Published online by Cambridge University Press:  24 October 2008

María Teresa Lozano
María Teresa Lozano
Affiliation:
Facultad de Ciencias, Universidad de Zaragoza, Spain
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Extract

The concept of arcbody was introduced in [4] as a generalization of prime tangles used by Lickorish[3] and Bleiler[l]. The pair (A, l), where A is a compact 3-manifold with boundary ∂A, and l is a 1-submanifold properly embedded in A, is an arcbody if:

(i) the inclusion ∂ A – l ↪ A – l is monic, i.e. A – l has incompressible boundary;

(ii) no component of (A, l) is homeomorphic to (D2, 0) × I or (D2, 0) × S1; and

(iii) every sphere of ∂A intersects l.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 1 , January 1987 , pp. 79 - 89
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

REFERENCES

[1]Bleiler., S. A.Knots prime on many strings. Trans. Amer. Math. Soc. 282 (1984), 385–402.Google Scholar
[2]Jaco., W.Adding a 2-handle to a 3-manifold: an application to property R. Proc. Amer. Math. Soc. 92 (1984), 288–292.Google Scholar
[3]Lickorish., W. B. R.Prime knots and tangles. Trans. Amer. Math. Soc. 267 (1981), 321–332.Google Scholar
[4]Lozano., M. T.Arcbodies. Math. Proc. Cambridge Philos. Soc. 94 (1983), 253–260.Google Scholar
[5]Lozano, M. T. and Przytycki., J.Incompressible surfaces in the exterior of a closed 3-braid. I. Math. Proc. Cambridge Philos. Soc. 98 (1985), 275–299.CrossRefGoogle Scholar
[6]Lyon., C. H.Incompressible surfaces in the boundary of a handlebody – an algorithm. Canad. J. Math. 32 (1980), 590–595.Google Scholar
[7]Rolfsen., D.Knots and Links (Publish or Perish, Inc., 1976).Google Scholar