6 citations · 11 across the 5 of their papers we have counts for
5 papers
Evolution of unknotting strategies for knots and braids
Nicholas Jackson, Colin G. Johnson
This paper explores the problem of unknotting closed braids and classical knots in mathematical knot theory. We apply evolutionary computation methods to learn sequences of moves t…
Twisted Alexander polynomials of hyperbolic knots
Nathan M. Dunfield, Stefan Friedl, Nicholas Jackson
We study a twisted Alexander polynomial naturally associated to a hyperbolic knot in an integer homology 3-sphere via a lift of the holonomy representation to SL(2, C). It is an un…
Approximations to the volume of hyperbolic knots
Stefan Friedl, Nicholas Jackson
We present computational data and heuristic arguments which suggest that given a hyperbolic knot the volume correlates with its determinant, the Mahler measure of its Alexander pol…
Rack and quandle homology
Nicholas Jackson
The theory of rack and quandle modules is developed - in particular a tensor product is defined, and shown to satisfy an appropriate adjointness condition. Notions of free rack and…
Extensions of racks and quandles
Nicholas Jackson
New definitions of rack and quandle modules are introduced, and shown to generalise the definitions previously studied by Andruskiewitsch, Etingof and Grana. This new construct is…