Virtual algebraic fibrations of surface-by-surface groups and orbits of the mapping class group

Robert Kropholler; Stefano Vidussi; Genevieve Walsh

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arXiv · 2103.06930

Virtual algebraic fibrations of surface-by-surface groups and orbits of the mapping class group

Robert Kropholler·Stefano Vidussi·Genevieve Walsh

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Abstract

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).

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Robert Kropholler, Stefano Vidussi, Genevieve Walsh. 2021-03-11. Virtual algebraic fibrations of surface-by-surface groups and orbits of the mapping class group. https://arxiv.org/abs/2103.06930

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