Mapping class groups of simply connected high-dimensional manifolds need not be arithmetic
| Autor: | Oscar Randal-Williams, Manuel Krannich |
|---|---|
| Přispěvatelé: | Krannich, Manuel [0000-0003-1994-5330], Randal-Williams, Oscar [0000-0002-7479-2878], Apollo - University of Cambridge Repository |
| Rok vydání: | 2020 |
| Předmět: |
Condensed Matter::Quantum Gases
Pure mathematics Statement (logic) General Mathematics 010102 general mathematics Geometric Topology (math.GT) Class (philosophy) 01 natural sciences Commensurability (mathematics) Mapping class group Manifold 57R50 11F06 20E26 Mathematics - Geometric Topology 0103 physical sciences Simply connected space FOS: Mathematics math.GT 010307 mathematical physics Meaning (existential) 0101 mathematics Mathematics Arithmetic group |
| Zdroj: | Comptes Rendus. Mathématique |
| ISSN: | 1778-3569 |
| DOI: | 10.5802/crmath.61 |
| Popis: | It is well known that Sullivan showed that the mapping class group of a simply connected high-dimensional manifold is commensurable with an arithmetic group, but the meaning of "commensurable" in this statement seems to be less well known. We explain why this result fails with the now standard definition of commensurability by exhibiting a manifold whose mapping class group is not residually finite. We do not suggest any problem with Sullivan's result: rather we provide a gloss for it. ERC, Leverhulme Trust |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|