On symmetric matrices associated with oriented link diagrams

  • Rinat Kashaev

    Université de Genève, Switzerland
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Abstract

Let be an oriented link diagram with the set of regions . We define a symmetric map (or matrix) : \( \operatorname{r}_{D}$$\times \) 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 , the negative signature of corrected by the writhe is conjecturally twice the Tristram– Levine signature function, where with being the indeterminate of the Alexander polynomial.