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FIBER QUADRISECANTS IN KNOT ISOTOPIES

T. FIEDLER

Laboratoire Emile Picard, Université Paul Sabatier, 118 Route Narbonne, 31062 Toulouse, France

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and

V. KURLIN

Department of Methematical Sciences, Durham University, Durham DH1 3LE, UK

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https://doi.org/10.1142/S0218216508006695Cited by:0 (Source: Crossref)

Abstract

Fix a straight line L in Euclidean 3-space and consider the fibration of the complement of L by half-planes. A generic knot K in the complement of L has neither fiber quadrisecants nor fiber extreme secants such that K touches the corresponding half-plane at 2 points. Both types of secants occur in generic isotopies of knots. We give lower bounds for the number of these fiber secants in all isotopies connecting given isotopic knots. The bounds are expressed in terms of invariants calculable in linear time with respect to the number of crossings.

Keywords:

AMSC: 57M25

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