Central stability for the homology of congruence subgroups and the second homology of Torelli groups
Central stability for the homology of congruence subgroups and the second homology of Torelli groups
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DOI：
10.1016/j.aim.2019.106740
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发表时间：
2017-04
影响因子：
1.7
通讯作者：
Jeremy Miller;Peter Patzt;Jenny Wilson
中科院分区：
文献类型：
--
作者：
Jeremy Miller;Peter Patzt;Jenny Wilson
证明了映射类群的Torelli子群的第二同调群和自由群的自同构群的表示稳定性结果。这加强了Boldsen-Hauge Dollerup和Day-Putman的结果。我们还证明了一个新的表示稳定性的结果，某些同余子群的同调，部分改进后的Putman-Sam的工作。这些结果遵循的一个一般性定理的syzygies某些模有限多项式次数。
We prove a representation stability result for the second homology groups of Torelli subgroups of mapping class groups and automorphism groups of free groups. This strengthens the results of Boldsen–Hauge Dollerup and Day–Putman. We also prove a new representation stability result for the homology of certain congruence subgroups, partially improving upon the work of Putman–Sam. These results follow from a general theorem on syzygies of certain modules with finite polynomial degree.