The Geometric Invariants of Group Extensions Part II: Split Extensions

Abstract

We compute the Ω^1(G) invariant when 1 {\to} H {\to} G {\to} K {\to} 1 is a split short exact sequence. We use this result to compute the invariant for pure and full braid groups on compact surfaces. Applications to twisted conjugacy classes and to finite generation of commutator subgroups are also discussed.

This paper has been withdrawn by the authors for further work on the main theorem

References in corpus (1)

• Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence

Cited by in corpus (1)

• The Geometric Invariants of Group Extensions