Scissor equivalence for torus links (Q2918797)

Given two oriented links in \(S^3\), consider all smooth cobordisms between the two links in \(S^3 \times [0,1]\) with no closed components. The cobordism distance between the two links is defined to be the absolute value of the maximal Euler characteristic of such a cobordism. The main result of this paper is to find, up to a bounded multiplicative error, the cobordism distance between two torus links, apart from an explicit set of exceptions. The expression for the distance is in terms of the genus and signature of each of the two links.NEWLINENEWLINEThe proof makes use of the Thom Conjecture, and also a result of \textit{C. McA. Gordon, R. A. Litherland} and \textit{K. Murasugi} [Can. J. Math. 33, 381--394 (1981; Zbl 0469.57004)]. In addition, various explicit cobordisms are given. These are built using two types of scissor cobordism (smoothing and saddle moves).