Simone Flaccovio

Uniform representations and character varieties of odd Turk's head knots

Let τ be the reflection reversing the order of the punctures in a p-punctured disc, with p odd. For any braid b such that K = closure(b(τbτ)) is a knot with det K > 1, I construct an SU(2) representation of the non-orientable mapping torus of bτ. Its restrictions to the fibre, th...

The volume-determinant inequality for Turk's head links

I prove the volume–determinant inequality for Turk's head links with p ≥ 3 strands and q ≥ 2 repetitions, including links with several components. The proof compares a geometric upper bound for volume with an analytic lower bound for the determinant. The diagram's periodic rotati...