Triple-crossing number, the genus of a knot or link and torus knots
Sign Up to like & getrecommendations! Published in 2020 at "Topology and its Applications"
DOI: 10.1016/j.topol.2020.107389
Abstract: Abstract We show that the triple-crossing number of any knot is greater or equal to twice its (canonical) genus and we show an even stronger bound in the case of links. As an application we… read more here.
Keywords: triple crossing; torus knots; genus; crossing number ... See more keywords
Donaldson-Thomas invariants, torus knots, and lattice paths
Sign Up to like & getrecommendations! Published in 2018 at "Physical Review D"
DOI: 10.1103/physrevd.98.026022
Abstract: In this paper, we find and explore the correspondence between quivers, torus knots, and combinatorics of counting paths. Our first result pertains to quiver representation theory—we find explicit formulas for classical generating functions and Donaldson-Thomas… read more here.
Keywords: generating functions; invariants torus; lattice paths; thomas invariants ... See more keywords