Span of the Bracket Polynomial and Triple-Crossing Projections of Knots by Jonah Greenberg '19

Span of the Bracket Polynomial and Triple-Crossing Projections of Knots by Jonah Greenberg ’19, Mathematics Senior Thesis Defense, Wednesday, May 8, 1 – 1:45 pm, Stetson Court Classroom 101

Abstract:  For double-crossing projections of knots, it is known that the span of the bracket polynomial is bounded above by 4c_2, where c_2 is the double crossing number of a knot and that this bound is achieved if and only if the knot is reduced and alternating. It is also known that the span of the bracket polynomial is bounded above by 8c_3. We are interested in when and how this bound is achieved, and will extend ideas about the bracket polynomial for double-crossing projections to triple-crossing projections along the way.