On symmetric matrices associated with oriented link diagrams

Original · EN

Let D be an oriented link diagram with the set of regions rD. We define a symmetric map (or matrix) τD× rD → Z[x] that gives rise to an invariant of oriented links, based on a slightly modified S-equivalence of Trotter and Murasugi in the space of symmetric matrices. In particular, for real x, the negative signature of τD corrected by the writhe is conjecturally twice the Tristram--Levine signature function, where 2x=√t+1√t with t being the indeterminate of the Alexander polynomial.