{"title":"The Euler characteristic of Out($F_n$)","authors":"M. Borinsky, K. Vogtmann","doi":"10.4171/CMH/501","DOIUrl":null,"url":null,"abstract":". We prove that the rational Euler characteristic of Out( F n ) is always negative and its asymptotic growth rate is Γ( n − 32 ) / √ 2 π log 2 n . This settles a 1987 conjecture of J. Smillie and the second author. We establish connections with the Lambert W -function and the zeta function.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":" ","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2019-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Commentarii Mathematici Helvetici","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/CMH/501","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 12
Abstract
. We prove that the rational Euler characteristic of Out( F n ) is always negative and its asymptotic growth rate is Γ( n − 32 ) / √ 2 π log 2 n . This settles a 1987 conjecture of J. Smillie and the second author. We establish connections with the Lambert W -function and the zeta function.
期刊介绍：
Commentarii Mathematici Helvetici (CMH) was established on the occasion of a meeting of the Swiss Mathematical Society in May 1928. The first volume was published in 1929. The journal soon gained international reputation and is one of the world''s leading mathematical periodicals.
Commentarii Mathematici Helvetici is covered in:
Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.
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