Virtual homological eigenvalues and the Weil-Petersson translation length  

作　　者：Yi Liu 

机构地区：[1]Beijing International Center for Mathematical Research,Peking University,Beijing 100871,China

出　　处：《Science China Mathematics》2023年第9期2119-2132,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11925101);National Key R&D Program of China(Grant No.2020YFA0712800)。

摘　　要：For any pseudo-Anosov automorphism on an orientable closed surface,an inequality is established by bounding certain growth of virtual homological eigenvalues with the Weil-Petersson translation length.The new inequality fits nicely with other known inequalities due to Kojima and McShane(2018)and Lê(2014).The new quantity to be considered is the square sum of the logarithmic radii of the homological eigenvalues(with multiplicity)outside the complex unit circle,called the homological Jensen square sum.The main theorem is as follows.For any cofinal sequence of regular finite covers of a given surface,together with lifts of a given pseudo-Anosov,the homological Jensen square sum of the lifts grows at most linearly fast compared with the covering degree,and the square root of the growth rate is at most 1/√4πtimes the Weil-Petersson translation length of the given pseudo-Anosov.

关 键 词：homological eigenvalue finite cover Weil-Petersson metric translation length 

分 类 号：O186.11[理学—数学]