martedi' 08-03-2005 (15:00) - Sala dei seminari Paolo Bellingeri (Pisa) : Surface braids II: finite type invariants

Argomento: Geometria

Starting with the classic braid group $B_n$, Birman and Baez have introduced the monoid $SB_n$ of singular braids where, in addition to the usual positive and negative crossings $\sg_i$ and $\sg_i^{-1}$ of the strands at position $i$ and $i+1$, one allows a singular crossing denoted $\tau_i$ where the two strands intersect. In the same way one can introduce the singular braid monoid on $\Sigma$, $SB_n(\Sigma)$, as an extension of the surface braid group $B_n (\Sigma)$. This monoid has been introduced by Gonz'alez-Meneses and Paris in order to define finite type (Goussarov- Vassiliev) invariants for surface braids. They constructed a universal finite type invariant for surface braids with integer coefficients. This result cannot be improved. We will show that there does not exist a universal finite type invariant for surface braids, which is also fonctorial, i.e. there does not exist a Kontsevich integral for surface braids. This result does not depend on the choice of the coefficient ring and it extends naturally to tangles on handlebodies. Finally we will discuss about the definition of finite type invariants for braid groups and their generalisations.

Giulia Curciarello Segreteria Didattica tel: 050-2213219 e-mail curciare@dm.unipi.it _______________________________________________ Settimanale mailing list Settimanale@mail.dm.unipi.it https://mail.dm.unipi.it/mailman/listinfo/settimanale