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Invariants of tangles

Published online by Cambridge University Press:  24 October 2008

Tim D. Cochran  and
Daniel Ruberman
Tim D. Cochran
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, U.S.A.
Daniel Ruberman
Affiliation:
Department of Mathematics, Brandeis University, Waltham, MA 02254, U.S.A.
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Extract

A tangle is a pair of strings (t0, t1) properly embedded in a 3-ball. Tangles have been used in several approaches to the classification of knots (see [1, 4, 15]). In these investigations, one keeps track of the endpoints of the arcs, so that the sum of two tangles along their boundaries is well defined. In particular, the sum of a given tangle with a trivial tangle, and any invariants of the resulting link, are invariants of the tangle under the restricted relation of isotopy keeping the endpoints fixed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 2 , March 1989 , pp. 299 - 306
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

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