Virtual algebraic fibrations of surface-by-surface groups and orbits of the mapping class group
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866917631887409152 |
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| author | Kropholler, Robert Vidussi, Stefano Walsh, Genevieve |
| author_facet | Kropholler, Robert Vidussi, Stefano Walsh, Genevieve |
| contents | We show that a conjecture of Putman--Wieland, which posits the nonexistence of finite orbits for higher Prym representations of the mapping class group, is equivalent to the existence of surface-by-surface and surface-by-free groups which do not virtually algebraically fiber. While the question about the existence of such groups remains open, we will show that there exist free-by-free and free-by-surface groups which do not algebraically fiber (hence fail to be virtually RFRS). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_06930 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Virtual algebraic fibrations of surface-by-surface groups and orbits of the mapping class group Kropholler, Robert Vidussi, Stefano Walsh, Genevieve Geometric Topology Group Theory We show that a conjecture of Putman--Wieland, which posits the nonexistence of finite orbits for higher Prym representations of the mapping class group, is equivalent to the existence of surface-by-surface and surface-by-free groups which do not virtually algebraically fiber. While the question about the existence of such groups remains open, we will show that there exist free-by-free and free-by-surface groups which do not algebraically fiber (hence fail to be virtually RFRS). |
| title | Virtual algebraic fibrations of surface-by-surface groups and orbits of the mapping class group |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2103.06930 |