Surface framed braids

TL;DR

This paper introduces the surface framed pure braid group, a topological generalization of the pure braid group on surfaces, providing new definitions and exploring their relations with existing braid group variants.

Contribution

It defines surface framed pure braid groups, offers multiple equivalent definitions, and studies their relationships with other surface braid groups.

Findings

Introduces the concept of surface framed braid groups.

Provides multiple equivalent definitions for these groups.

Analyzes exact sequences relating surface framed braid groups to other braid groups.

Abstract

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.