{"title":"具有方形可求和菱形剪切的圆同构","authors":"Dragomir Šarić, Yilin Wang, Catherine Wolfram","doi":"10.1093/imrn/rnae155","DOIUrl":null,"url":null,"abstract":"We introduce and study the space of homeomorphisms of the circle (up to Möbius transformations), which are in $\\ell ^{2}$ with respect to modular coordinates called diamond shears along the edges of the Farey tessellation. Diamond shears are related combinatorially to shear coordinates and are also closely related to the $\\log \\Lambda $-lengths of decorated Teichmüller space introduced by Penner. We obtain sharp results comparing this new class to the Weil–Petersson class and Hölder classes of circle homeomorphisms. We also express the Weil–Petersson metric tensor and symplectic form in terms of infinitesimal shears and diamond shears.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":"82 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Circle Homeomorphisms with Square Summable Diamond Shears\",\"authors\":\"Dragomir Šarić, Yilin Wang, Catherine Wolfram\",\"doi\":\"10.1093/imrn/rnae155\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce and study the space of homeomorphisms of the circle (up to Möbius transformations), which are in $\\\\ell ^{2}$ with respect to modular coordinates called diamond shears along the edges of the Farey tessellation. Diamond shears are related combinatorially to shear coordinates and are also closely related to the $\\\\log \\\\Lambda $-lengths of decorated Teichmüller space introduced by Penner. We obtain sharp results comparing this new class to the Weil–Petersson class and Hölder classes of circle homeomorphisms. We also express the Weil–Petersson metric tensor and symplectic form in terms of infinitesimal shears and diamond shears.\",\"PeriodicalId\":14461,\"journal\":{\"name\":\"International Mathematics Research Notices\",\"volume\":\"82 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-07-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Mathematics Research Notices\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1093/imrn/rnae155\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Mathematics Research Notices","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/imrn/rnae155","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Circle Homeomorphisms with Square Summable Diamond Shears
We introduce and study the space of homeomorphisms of the circle (up to Möbius transformations), which are in $\ell ^{2}$ with respect to modular coordinates called diamond shears along the edges of the Farey tessellation. Diamond shears are related combinatorially to shear coordinates and are also closely related to the $\log \Lambda $-lengths of decorated Teichmüller space introduced by Penner. We obtain sharp results comparing this new class to the Weil–Petersson class and Hölder classes of circle homeomorphisms. We also express the Weil–Petersson metric tensor and symplectic form in terms of infinitesimal shears and diamond shears.
期刊介绍:
International Mathematics Research Notices provides very fast publication of research articles of high current interest in all areas of mathematics. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics.