Partial Torelli groups and homological stability

IF 0.6 3区 数学 Q3 MATHEMATICS Algebraic and Geometric Topology Pub Date : 2023-11-05 DOI:10.2140/agt.2023.23.3417
Andrew Putman
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引用次数: 2

Abstract

We prove a homological stability theorem for the subgroup of the mapping class group acting as the identity on some fixed portion of the first homology group of the surface. We also prove a similar theorem for the subgroup of the mapping class group preserving a fixed map from the fundamental group to a finite group, which can be viewed as a mapping class group version of a theorem of Ellenberg-Venkatesh-Westerland about braid groups. These results require studying various simplicial complexes formed by subsurfaces of the surface, generalizing work of Hatcher-Vogtmann.
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部分Torelli群与同调稳定性
证明了映射类群的子群在平面的第一同调群的某固定部分上作为恒等的一个同调稳定性定理。对于映射类群的子群,我们也证明了一个类似的定理,该定理保持了从基本群到有限群的固定映射,可以看作是关于辫群的Ellenberg-Venkatesh-Westerland定理的映射类群版本。这些结果需要研究由表面的次表面形成的各种简单配合物,推广Hatcher-Vogtmann的工作。
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来源期刊
CiteScore
1.10
自引率
14.30%
发文量
62
审稿时长
6-12 weeks
期刊介绍: Algebraic and Geometric Topology is a fully refereed journal covering all of topology, broadly understood.
期刊最新文献
Partial Torelli groups and homological stability Connective models for topological modular forms of level n The upsilon invariant at 1 of 3–braid knots Cusps and commensurability classes of hyperbolic 4–manifolds On symplectic fillings of small Seifert 3–manifolds
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