ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 18, 20, 55, 57 Vershinin, Vladimir, Sobolev Institute of Mathematics, Novosibirsk, Russia Generalizations of Braids: Homology and Vassiliev Invariants We consider the following generalizations of braids: braid group in a handlebody of the genus g and singular braids: the braid-permutation group BP_{n} and the Baez-Birman monoid SB_{n}, (or singular braid monoid). The braidpermutation group BP_{n} is the subgroup of the group of automorphisms of a free group AutF_{n}, generated by the symmetric group Σ_{n} and the braid group, considered as subgroups of AutF_{n}. Their homological properties are studied. Applications to the theory of Vassiliev invariants are obtained. Reference: V. V. Vershinin, Generalizations of braids from homological point of view, in Proceedings of the 10th Siberian Summer School on Algebra and Analysis. Inst. of Math., Novosibirsk, (1997), 40-62 (Russian).