Generators for the Pure Symmetric Outer Automorphisms of a Free Product
Harry Iveson
TL;DR
This paper constructs a specialized subcomplex of Outer Space to provide a geometric proof that pure symmetric outer automorphisms of a free product are generated by factor and Whitehead automorphisms relative to a splitting.
Contribution
It introduces a new geometric approach to understanding generators of pure symmetric outer automorphisms in free products.
Findings
Established a geometric proof for the generation of automorphisms
Constructed a 'nice' subcomplex of Outer Space
Identified generators as factor and Whitehead automorphisms
Abstract
We construct a `nice' subcomplex of the Outer Space for a free product in order to give a geometric proof that the pure symmetric outer automorphisms of a given splitting of a free product are generated by factor outer automorphisms and Whitehead outer automorphisms relative to the splittting.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Rings, Modules, and Algebras