Locally Moving Groups and the Reconstruction Problem for Chains and Circles

Abstract

We prove that complete Boolean algebras can be reconstructed from any locally moving subgroup of their full automorphism group. We use this theorem in order to prove that linear orders and circles can be reconstructed from small subgroups of their full automorphism groups.

171 pages

References in corpus (2)

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

Cited by in corpus (7)

• The chameleon groups of Richard J. Thompson: automorphisms and dynamics
• Automorphisms of generalized Thompson groups
• Twisted conjugacy in Richard Thompson's group T
• Commensurations and Subgroups of Finite Index of Thompson's Group F
• Automatic Homeomorphicity of Locally Moving Clones
• The Reconstruction of Cycle-free Partial Orders from their Abstract Automorphism Groups II : Cone Transitive CFPOs
• On a stronger reconstruction notion for monoids and clones