Deformation spaces of $G$-trees and automorphisms of Baumslag–Solitar groups | Zendy

Matt Clay | Zendy

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Deformation spaces of $G$-trees and automorphisms of Baumslag–Solitar groups

Author(s) -

Matt Clay

Publication year - 2009

Publication title -

groups geometry and dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.05

H-Index - 25

eISSN - 1661-7215

pISSN - 1661-7207

DOI - 10.4171/ggd/51

Subject(s) - automorphism , mathematics , computation , finitely generated abelian group , algebraic number , invariant (physics) , pure mathematics , automorphism group , combinatorics , mathematical analysis , algorithm , mathematical physics

We construct an invariant deformation retract of a deformation space ofG-trees. We show that this complex is finite dimensional in certain cases andprovide an example that is not finite dimensional. Using this complex wecompute the automorphism group of the classical non-solvable Baumslag-Solitargroups BS(p,q). The most interesting case is when p properly divides q. Collinsand Levin computed a presentation for Aut(BS(p,q)) in this case using algebraicmethods. Our computation uses Bass-Serre theory to derive these presentations.Additionally, we provide a geometric argument showing Out(BS(p,q)) is notfinitely generated when p properly divides q.

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