A Geometric Proof of the Structure Theorem for Cyclic Splittings of Free Groups

Abstract

We give a geometric proof of a well known theorem that describes splittings of a free group as an amalgamated product or HNN extension over the integers. The argument generalizes to give a similar description of splittings of a virtually free group over a virtually cyclic group.

11 pages, v2 added a reference

References in corpus (2)

• The Grushko decomposition of a finite graph of finite rank free groups: an algorithm
• Krull dimension for limit groups III: Scott complexity and adjoining roots to finitely generated groups

Cited by in corpus (3)

• On the one-endedness of graphs of groups
• Generalized chordality, vertex separators and hyperbolicity on graphs
• Quotient and blow-up of automorphisms of graphs of groups