# 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} }

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…

## One Citation

### The Levine-Tristram Signature: A Survey

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The Levine-Tristram signature associates to each oriented link L in S3 a function σL: S1 → \( {\mathbb{z}} \). This invariant can be defined in a variety of ways, and its numerous applications…

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