Fiber quadrisecants in knot isotopies

Fiedler, T.; Kurlin, V.

doi:10.1142/s0218216508006695

Fiber quadrisecants in knot isotopies

Fiedler, T.; Kurlin, V.

Authors

T. Fiedler

V. Kurlin

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.

Citation

Fiedler, T., & Kurlin, V. (2008). Fiber quadrisecants in knot isotopies. Journal of Knot Theory and Its Ramifications, 17(11), 1415-1428. https://doi.org/10.1142/s0218216508006695

Journal Article Type	Article
Publication Date	Nov 1, 2008
Deposit Date	Apr 4, 2011
Journal	Journal of Knot Theory and Its Ramifications
Print ISSN	0218-2165
Electronic ISSN	1793-6527
Publisher	World Scientific Publishing
Peer Reviewed	Peer Reviewed
Volume	17
Issue	11
Pages	1415-1428
DOI	https://doi.org/10.1142/s0218216508006695
Keywords	Knot, Braid, Isotopy, Fiber quadrisecant, Fiber extreme secant, Writhe, Trace graph, 1-parameter approach, Higher order Reidemeister theorem.