Nestor Colin, Rita Jiménez Rolland, Porfirio L. León Álvarez, Luis Jorge Sánchez Saldaña
{"title":"On the dimension of Harer's spine for the decorated Teichmüller space","authors":"Nestor Colin, Rita Jiménez Rolland, Porfirio L. León Álvarez, Luis Jorge Sánchez Saldaña","doi":"arxiv-2409.04392","DOIUrl":null,"url":null,"abstract":"In \\cite{Ha86} Harer explicitly constructed a spine for the decorated\nTeichm\\\"uller space of orientable surfaces with at least one puncture and\nnegative Euler characteristic. In this paper we point out some instances where\nhis computation of the dimension of this spine is off by $1$ and give the\ncorrect dimension.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":"2 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.04392","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In \cite{Ha86} Harer explicitly constructed a spine for the decorated
Teichm\"uller space of orientable surfaces with at least one puncture and
negative Euler characteristic. In this paper we point out some instances where
his computation of the dimension of this spine is off by $1$ and give the
correct dimension.