arXiv subjects

Jan A. Kneissler

Publications and source records attributed to Jan A. Kneissler.

2 recordsLinked to original sources

arXiv1997

The number of primitive Vassiliev invariants up to degree 12

We present algorithms giving upper and lower bounds for the number of independent primitive rational Vassiliev invariants of degree m modulo those of degree m-1. The values have been calculated for the formerly unknown degrees m = 10, 11, 12. Upper and lower bounds coincide, which reveals that all Vassiliev invariants of degree smaller 13 are orientation insensitive and are coming from representations of Lie algebras so and gl. Furthermore, a conjecture of Vogel is falsified and it is shown that the Λ-module of connected trivalent diagrams (Chinese characters) is not free.

q-alg↗

arXiv1995

Woven Braids and their Closures

A special class of braids, called woven, is introduced and it is shown that every conjugation class of the braid group contains woven braids. In consequence, links can be presented as plats or closures of woven braids. Restricting on knots, we get the 'woven version' of the well-known theorem of Markov, giving moves that are capable of producing all woven braids with equivalent closures. As corollary we obtain that a link in which each component is dyed with at least two colours can be projected onto a plane without crossing strands of the same colour. Finally a table of minimal woven braids for all nine crossing knots is appended.

q-alg↗