# On symmetric matrices associated with oriented link diagrams

@article{Kashaev2021OnSM,
title={On symmetric matrices associated with oriented link diagrams},
author={Rinat M. Kashaev},
journal={Topology and Geometry},
year={2021}
}
• R. Kashaev
• Published 15 January 2018
• Mathematics
• Topology and Geometry
Let $D$ be an oriented link diagram with the set of regions $\operatorname{r}_{D}$. We define a symmetric map (or matrix) $\operatorname{\tau}_{D}\colon\operatorname{r}_{D}\times \operatorname{r}_{D} \to \mathbb{Z}[x]$ 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 $\operatorname{\tau}_{D}$ corrected by the writhe is conjecturally…
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