The co-Hopfian property of surface braid groups

TL;DR

This paper investigates the co-Hopfian property of surface braid groups, showing that any finite index subgroup is co-Hopfian by analyzing injective homomorphisms within these groups.

Contribution

It characterizes injective homomorphisms of finite index subgroups of surface pure braid groups and establishes their co-Hopfian property.

Findings

Any injective homomorphism from a finite index subgroup into the group is described.

Any finite index subgroup of the surface braid group is co-Hopfian.

Provides structural insights into surface braid groups.

Abstract

Let g and n be integers at least two, and let G be the pure braid group with n strands on a closed orientable surface of genus g. We describe any injective homomorphism from a finite index subgroup of G into G. As a consequence, we show that any finite index subgroup of G is co-Hopfian.