Classification of stable surfaces with respect to automatic continuity
Abstract
Abstract We provide a complete classification of when the homeomorphism group of a stable surface, normal upper Sigma Σ $\Sigma$ , has the automatic continuity property: Any homomorphism from normal upper H normal o normal m normal e normal o left parenthesis normal upper Sigma right parenthesis H o m e o ( Σ ) $\mathrm{Homeo}({\Sigma})$ to a separable group is necessarily continuous. This result descends to a classification of when the mapping class group of normal upper Sigma Σ $\Sigma$ has the automatic continuity property. Towards this classification, we provide a general framework for proving automatic continuity for groups of homeomorphisms. Applying this framework, we also show that the homeomorphism group of any stable, second-countable Stone space has the automatic continuity property. Under the presence of stability, this answers two questions of Mann.
Fields of Study & Subjects
Advanced Numerical Analysis Techniques
Tribology and Lubrication Engineering
Advanced Theoretical and Applied Studies in Material Sciences and Geometry
Publication details
- Journal / source
- Compositio Mathematica
- Publisher
- Cambridge University Press (CUP)
- Volume
- 162
- Issue
- 3
- Pages
- 669–702
- Publication date
- 1 March 2026
- Language
- EN