On groups $G_{n}^{k},$ braids and Brunnian braidsстатья
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Дата последнего поиска статьи во внешних источниках: 17 апреля 2018 г.
Аннотация:In [V. O. Manturov, arXiv:1501.05208v1], the second author defined the k-free braid group with n strands Gkn. These groups appear naturally as groups describing dynamical systems of n particles in some “general position”. Moreover, in [V. O. Manturov and I. M. Nikonov, J. Knot Theory Ramification 24 (2015) 1541009] the second author and Nikonov showed that Gkn is closely related to classical braids. The authors showed that there are homomorphisms from the pure braids group on n strands to G3n and G4n and they defined homomorphisms from Gkn to the free products of ℤ2. That is, there are invariants for pure free braids by G3n and G4n.
On the other hand in [D. A. Fedoseev and V. O. Manturov, J. Knot Theory Ramification 24(13) (2015) 1541005, 12 pages] Fedoseev and the second author studied classical braids with addition structures: parity and points on each strands. The authors showed that the parity, which is an abstract structure, has geometric meaning — points on strands. In [S. Kim, arXiv:submit/1548032], the first author studied G2n with parity and points. the author constructed a homomorphism from G2n+1 to the group G2n with parity.
In the present paper, we investigate the groups G3n and extract new powerful invariants of classical braids from G3n. In particular, these invariants allow one to distinguish the non-triviality of Brunnian braids.
Read More: https://www.worldscientific.com/doi/abs/10.1142/S0218216516500784