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… 

Figures from this paper

The Levine-Tristram Signature: A Survey

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

References

SHOWING 1-9 OF 9 REFERENCES

The Burau representation is unitary

A slight modification of the Burau representation of the braid group is shown to be unitary relative to an explicitly defined Hermitian form. This gives a partial answer to the problem of identifying

Some cobordism invariants for links

  • A. Tristram
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1969
The purpose of this paper is to obtain some necessary conditions for a link in Euclidean 3-space to be spanned by a locally unknotted surface of given type in one half of 4-space. In particular

Invariants of knot cobordism

The Gottingen State and University Library provides access to digitized documents strictly for noncommercial educational, research and private purposes and makes no warranty with regard to their use

Exactly solved models in statistical mechanics

exactly solved models in statistical mechanics exactly solved models in statistical mechanics rodney j baxter exactly solved models in statistical mechanics exactly solved models in statistical

Homology of Group Systems With Applications to Knot Theory

On knot invariants related to some statistical mechanical models

On utilise trois sortes differentes de modeles de mecanique statistique pour construire des invariants de nœuds. Les modeles de sommets emergent comme les plus generaux

Metaplectic link invariants

ON A CERTAIN NUMERICAL INVARIANT OF LINK TYPES

Cyclotomic invariants for links