The goal of this dissertation is to develop the formulation of the average minimal genus of all reduced alternating rational links with a given crossing number. Work has been done by N. Dunfield to approximate the growth of the genus of knots with...
This dissertation introduces new invariants for a large class of links in knot theory, called alternating links. It also analyzes the strength of these invariants, that we call writhe-like invariants, in comparison with a few general link invarian...
A long-standing problem in knot theory concerns the additivity of crossing numbers of links under the connected sum operation. It is conjectured that if L1 and L2 are links, then Cr(L1#L2)=Cr(L1)+Cr(L2), but so far this has been proved only for ce...
