teichm曲线的模符号

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-05-12 DOI:10.1515/crelle-2021-0019

C. McMullen

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引用次数: 7

摘要

摘要本文引入了一个附加于任意双曲黎曼曲面V上的非abel模符号𝒮(V){{\mathcal{S}}(V)}空间，并应用它得到了关于多边形台球和全纯1型的新结果。特别地，它证明了正多边形中台球周期轨迹的刻痕行为是由一组同胚于ωω+1{\ ω ^{\ ω}+1}的可数测度控制的。

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Modular symbols for Teichmüller curves

Abstract This paper introduces a space of nonabelian modular symbols 𝒮⁢(V){{\mathcal{S}}(V)} attached to any hyperbolic Riemann surface V, and applies it to obtain new results on polygonal billiards and holomorphic 1-forms. In particular, it shows the scarring behavior of periodic trajectories for billiards in a regular polygon is governed by a countable set of measures homeomorphic to ωω+1{\omega^{\omega}+1}.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.