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Constructions of arcbodies

Published online by Cambridge University Press:  24 October 2008

María Teresa Lozano
Facultad de Ciencias, Universidad de Zaragoza, Spain


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 ∂ AlAl is monic, i.e. Al 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.

Research Article
Copyright © Cambridge Philosophical Society 1987

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