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A Primer on Mapping Class Groups (Pms-49)
- Publisher
- Wiley
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/blms/bdw016
- Publisher site
- See Article on Publisher Site
Abstract
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 σ of the surface braid group Bn(S) to Diff(S,n), the group of 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.
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Jun 1, 2016