The chameleon groups of Richard J. Thompson: automorphisms and dynamics

Abstract

The automorphism groups of several of Thompson's countable groups of piecewise linear homeomorphisms of the line and circle are computed and it is shown that the outer automorphism groups of these groups are relatively small. These results can be interpreted as stability results for certain structures of PL functions on the circle. Machinery is developed to relate the structures on the circle to corresponding structures on the line.

References in corpus (1)

• Locally Moving Groups and the Reconstruction Problem for Chains and Circles

Cited by in corpus (33)

• Automorphisms of generalized Thompson groups
• Central extensions of the Ptolemy-Thompson group and quantized Teichmuller theory
• Algorithms and Classification in Groups of Piecewise-Linear Homeomorphisms
• Locally Moving Groups and the Reconstruction Problem for Chains and Circles
• Growth of the asymptotic dimension function for groups
• Jones representations of Thompson's group $F$ arising from Temperley-Lieb-Jones algebras
• Isomorphisms of Brin-Higman-Thompson groups
• Twisted conjugacy in Richard Thompson's group T
• Geometric quasi-isometric embeddings into Thompson's group F
• Commensurations and Subgroups of Finite Index of Thompson's Group F
• Subgroup dynamics and $C^{\ast }$-simplicity of groups of homeomorphisms
• Infinitely supported Liouville measures of Schreier graphs
• The further chameleon groups of Richard Thompson and Graham Higman: Automorphisms via dynamics for the Higman groups $G_{n,r}$
• The Sigma Invariants of Thompson's Group F
• A short proof of Rubin's theorem
• The conjugacy problem in extensions of Thompson's group F
• From symmetries of the modular tower of genus zero real stable curves to an Euler class for the dyadic circle
• Thompson-like groups, Reidemeister numbers, and fixed points
• Rank and deficiency gradients of generalised Thompson groups of type F
• Twisted conjugacy classes in R. Thompson's group F
• The infinite associahedron and R.J. Thompson's group T
• On Jones' connections between subfactors, conformal field theory, Thompson's groups and knots
• Reversibility and Banach Algebras
• A family of non-isomorphism results
• Reconstruction theorem for homeomorphism groups without small sets and non-shrinking functions of a normed space
• 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
• Automorphisms of the generalised Thompson's group $T_{n,r}$
• On the automorphism group of the asymptotic pants complex of a planar surface of infinite type
• Public key cryptography based on some extensions of group
• Addendum to "Commensurations and Subgroups of Finite Index of Thompson's Group F"
• Growth of positive words and lower bounds of the growth rate for Thompson's groups $F(p)$