Automorphisms of generalized Thompson groups

Abstract

We look at the automorphisms of Thompson type groups of piecewise linear homeomorphisms of the real line or circle that use slopes that are integral powers of a fixed integer n with n>2. We show that large numbers of "exotic" automorphisms appear---automorphisms that are represented as conjugation by non-PL homeomorphisms of the real line or circle. This is in contrast to the n=2 case where no such automorphisms appear.

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References in corpus (3)

• The chameleon groups of Richard J. Thompson: automorphisms and dynamics
• The ubiquity of Thompson's group F in groups of piecewise linear homeomorphisms of the unit interval
• Locally Moving Groups and the Reconstruction Problem for Chains and Circles

Cited by in corpus (23)

• The Algebra of Strand Splitting. II. A Presentation for the Braid Group on One Strand
• A geometric classification of some solvable groups of homeomorphisms
• Elementary amenable subgroups of R. Thompson's group F
• Locally Moving Groups and the Reconstruction Problem for Chains and Circles
• The Free Group of Rank 2 is a Limit of Thompson's Group F
• Twisted conjugacy in Richard Thompson's group T
• The further chameleon groups of Richard Thompson and Graham Higman: Automorphisms via dynamics for the Higman groups $G_{n,r}$
• A short proof of Rubin's theorem
• The conjugacy problem in extensions of Thompson's group F
• Rank and deficiency gradients of generalised Thompson groups of type F
• An $n$-adic generalization of the Lodha-Moore group
• Thompson-like groups, Reidemeister numbers, and fixed points
• Semi-simple actions of the Higman-Thompson groups $T_n$ on finite-dimensional CAT(0) spaces
• Reconstruction theorem for homeomorphism groups without small sets and non-shrinking functions of a normed space
• Automorphisms of the generalised Thompson's group $T_{n,r}$
• An automata theoretic proof that $\mathrm{Out}(T)\cong \mathbb{Z}/2\mathbb{Z}$ and some embedding results for $\mathrm{Out}(V)$
• The automorphism group of Thompson's group F: subgroups and metric properties
• A Description of Aut(dVn) and Out(dVn) Using Transducers
• Sigma 1 of PL-homeomorphism groups
• Metrics and embeddings of generalizations of Thompson's group F
• Tamari lattices, forests and Thompson monoids
• A Minimal Non-solvable Group of Homeomorphisms
• Twisted conjugacy in generalized Thompson groups of type F