ИСТИНА

In [2] V.O.Manturov dened the k-free braid group with n strands Gkn. These groupsappear naturally as groups describing dynamical systems of n particles in some general position". Moreover, in [3] V.O.Manturov and I.M.Nikonov showed that Gk n is closely related classical braids. The authors showed that there are homomorphisms from the pure braids group on n strands to G3n and G4n and they dened homomorphisms from Gkn to the free product of Z2, which give `indices to each crossing. In this talk, we investigate new invariant of classical braids, which is constructed from `indices`. In particular, these invariants allow one to distinguish the non-triviality of Brunnian braids. In the last of the talk, we talk about the group Gkn, roughly speaking, which is generated by `triple points and `classical crossings.