Surface framed braids

Paolo Bellingeri (1) , Sylvain Gervais (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 LMJL - Laboratoire de Mathématiques Jean Leray

In this paper we introduce the framed pure braid group on $n$ strands of an oriented surface, a topological generalisation of the pure braid group $P_n$. We give different equivalents definitions for framed pure braid groups and we study exact sequences relating these groups with other generalisations of $P_n$, usually called surface pure braid groups. The notion of surface framed braid groups is also introduced.

Mots clés: Braids; Surface; Mapping class groups

Domaines: Topologie géométrique [math.GT]

Paolo Bellingeri, Sylvain Gervais. Surface framed braids. Geometriae Dedicata, 2012, 159, pp.51-69. ⟨hal-00450226v2⟩