Symplectic groups, mapping class groups and the stability of bounded cohomology

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-08-05 DOI:10.1016/j.topol.2025.109531

Thorben Kastenholz

引用次数: 0

Abstract

Mapping class groups satisfy cohomological stability. In this note we show how results by Bestvina and Fujiwara imply that their bounded cohomology does not stabilize, additionally we show that stabily polynomials in the Mumford-Morita-Miller classes are unbounded i.e. their norm tends to infinity as one increases the genus.

While the bounded cohomology of the symplectic group does stabilize, we show that it does not stabilize via isometries in degree 2. In order to establish this we calculate the norm of the signature class in

{Sp}_{2 h} (R)

and estimate the norm of the integral signature class.

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辛群，映射类群与有界上同调的稳定性

映射类群满足上同调稳定性。在这篇文章中，我们展示了Bestvina和Fujiwara的结果如何暗示他们的有界上同不稳定，另外我们还展示了Mumford-Morita-Miller类中的稳定多项式是无界的，即当一个人增加属时，它们的范数趋于无穷。虽然辛群的有界上同调是稳定的，但我们证明了它在2次等距上是不稳定的。为了证明这一点，我们计算了Sp2h(R)中签名类的范数，并估计了积分签名类的范数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.