FIBER QUADRISECANTS IN KNOT ISOTOPIES

Fiedler, T and Kurlin, V ORCID: 0000-0001-5328-5351 (2008) FIBER QUADRISECANTS IN KNOT ISOTOPIES. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 17 (11). pp. 1415-1428.

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Official URL: http://dx.doi.org/10.1142/s0218216508006695

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.

Item Type:	Article
Additional Information:	12 pages, 8 figures
Uncontrolled Keywords:	Knot, braid, isotopy, fiber quadrisecant, fiber extreme secant, writhe, trace graph, 1-parameter approach, higher order Reidemeister theorem
Depositing User:	Symplectic Admin
Date Deposited:	14 Dec 2016 15:47
Last Modified:	19 Jan 2023 07:24
DOI:	10.1142/S0218216508006695
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3004873