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ON SEIFERT CIRCLES AND FUNCTORS FOR TANGLES

H. C. LEE

Theoretical Physics Branch, Chalk River Laboratories, AECL Research, Chalk River, Ontario, Canada K0J 1J0, Canada

Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada N6A 6B9, Canada

This work is supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada and a grant from the Commemorative Association for the Japan World Exposition (1970).

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https://doi.org/10.1142/S0217751X9200394XCited by:4 (Source: Crossref)

Abstract

The properties of the Seifert circles in an oriented tangle diagram are exploited to prove a theorem that asserts that every (n,n)-tangle diagram is isotopic to a partially closed braid, and a second one that facilitates the assignment of wrong-way edges, one on each Seifert circle, in a tangle diagram. These result are used to identify the structure of an abstract algebra on which a functor for the isotopy of general tangles may be constructed. Any finite dimensional irreducible representation of a quasitriangular Hopf algebra is a realization of this algebra.