Geometrically and diagrammatically maximal knots

Abhijit Champanerkar, CUNY Staten Island

Abstract: In this talk, we study sequences of knots for which the hyperbolic volume per crossing and the determinant per crossing are asymptotically maximal. One such family is weaving knots, which are alternating knots with the same projection as torus knots. Using angle structures, we provide asymptotically correct volume bounds for weaving knots. Applying geometric techniques of Agol, we construct more general families of geometrically and diagrammatically maximal knots. This is joint work with Ilya Kofman and Jessica Purcell.