Published August 2019
| Version Submitted
Journal Article
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Surjective homomorphisms between surface braid groups
Abstract
Let PB_n(S_(g,p)) be the pure braid group of a genus g > 1 surface with p punctures. In this paper we prove that any surjective homomorphism PB_n(S_(g,p)) → PB_m(S_(g,p)) factors through one of the forgetful homomorphisms. We then compute the automorphism group of PB_m(S_(g,p)), which gives a simpler proof of Irmak–Ivanov–McCarthy [IIM03, Theorem 1]. Surprisingly, in contrast to the n = 1 case, any automorphism of PB_n(S_(g,p)) for n > 1 is geometric.
Additional Information
© 2019 The Hebrew University of Jerusalem. Received April 26, 2017 and in revised form July 12, 2018. First Online: 27 May 2019. The author is grateful to anonymous referees and Maxime Bergeron for suggestions on the writing. She would also like to extend her warmest thanks to Benson Farb for his extensive comments and for his invaluable support from start to finish.Attached Files
Submitted - 1704.05142.pdf
Files
1704.05142.pdf
Additional details
Identifiers
- Eprint ID
- 95821
- DOI
- 10.1007/s11856-019-1881-7
- Resolver ID
- CaltechAUTHORS:20190528-131032719
Related works
- Describes
- 10.1007/s11856-019-1881-7 (DOI)
- https://arxiv.org/abs/1704.05142 (URL)
Dates
- Created
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2019-05-28Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field