On the non-realizability of braid groups by diffeomorphisms
| Autor: | Nick Salter, Bena Tshishiku |
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| Rok vydání: | 2016 |
| Předmět: |
0209 industrial biotechnology
Pure mathematics General Mathematics 010102 general mathematics Braid group Geometric Topology (math.GT) Group Theory (math.GR) 02 engineering and technology 01 natural sciences Lift (mathematics) Mathematics - Geometric Topology 020901 industrial engineering & automation Realizability FOS: Mathematics 0101 mathematics Mathematics - Group Theory Spherical motion Mathematics |
| Zdroj: | Bulletin of the London Mathematical Society. 48:457-471 |
| ISSN: | 1469-2120 0024-6093 |
| DOI: | 10.1112/blms/bdw016 |
| Popis: | For every compact surface $S$ of finite type (possibly with boundary components but without punctures), we show that when $n$ is sufficiently large there is no lift $\sigma$ of the surface braid group $B_n(S)$ to $\operatorname{Diff}(S,n)$, the group of $C^1$ diffeomorphisms preserving $n$ marked points and restricting to the identity on the boundary. Our methods are applied to give a new proof of Morita's non-lifting theorem in the best possible range. These techniques extend to the more general setting of spaces of codimension-$2$ embeddings, and we obtain corresponding results for spherical motion groups, including the string motion group. Comment: This version incorporates a number of improvements as suggested by an anonymous referee. Of primary interest among this is the inclusion of a new proof of the Morita non-lifting theorem for $C^1$ diffeomorphisms for all $g\ge 2$ |
| Databáze: | OpenAIRE |
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