| Popis: |
We give a construction of Gusarov's groups [Gscr ] n of knots based on pure braid commutators, and show that any element of [Gscr ] n is represented by an infinite number of prime alternating knots of braid index less than or equal to n +1. We also study [Vscr ] n , the torsion-free part of [Gscr ] n , which is the group of equivalence classes of knots which cannot be distinguished by any rational Vassiliev invariant of order less than or equal to n . Generalizing the Gusarov–Ohyama definition of n -triviality, we give a characterization of the elements of the n th group of the lower central series of an arbitrary group. |
