In this paper, we study representations of $G_{n}^{3}$ -like groups. The group $G_{n}^{3}$ itself appeared in works of the third named author on non-Reidemeister knot (and braid) theory. This group is closely related to dynamical systems of points and their invariants. Representations of $G_{n}^{3}$ -like groups are useful both for the study of those groups themselves, and constructing invariants of knots and braids based on the $G_{n}^{3}$ -like group structure.

Keywords:

AMSC: 57M25, 57M27

References

1. J. S. Birman, On the stable equivalence of plat representations of knots and links, Canad. J. Math. 28(2) (1976) 264–290. Crossref, Web of Science, Google Scholar
2. D. P. Ilyutko, V. O. Manturov and I. M. Nikonov, Parity in knot theory and graph-links, J. Math. Sci. 193 (2013) 809–965. Crossref, Google Scholar
3. D. P. Ilyutko, V. O. Manturov and I. M. Nikonov, Parity and Patterns in Low-Dimensional Topology (Cambridge Science Publishers, 2015). Google Scholar
4. V. O. Manturov, Non-Reidemeister knot theory and its applications in dynamical systems, geometry, and topology, preprint (2015), arXiv:1501.05208. Google Scholar
5. V. O. Manturov, D. A. Fedoseev, S. Kim and I. M. Nikonov, Invariants and Pictures: Low-Dimensional Topology and Combinatorial Group Theory (World Scientific, Singapore, 2020). Link, Google Scholar
6. R. L. Rubinsztein, Topological quandles and invariants of links, J. Knot Theory Ramifications 16(6) (2007) 789–808. Link, Web of Science, Google Scholar