Abelian quotients of mapping class groups of highly connected manifolds

被引：17

作者：

Galatius, Soren ^{[1
]}

Randal-Williams, Oscar ^{[2
]}

机构：

[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[2] Ctr Math Sci, Wilberforce Rd, Cambridge CB3 0WB, England

来源：

MATHEMATISCHE ANNALEN | 2016年 / 365卷 / 1-2期

基金：

美国国家科学基金会; 新加坡国家研究基金会;

关键词：

HOMOTOPY GROUPS; PL/O; BPL;

D O I：

10.1007/s00208-015-1300-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We compute the abelianisations of the mapping class groups of the manifolds for and . The answer is a direct sum of two parts. The first part arises from the action of the mapping class group on the middle homology, and takes values in the abelianisation of the automorphism group of the middle homology. The second part arises from bordism classes of mapping tori and takes values in the quotient of the stable homotopy groups of spheres by a certain subgroup which in many cases agrees with the image of the stable J-homomorphism. We relate its calculation to a purely homotopy theoretic problem.

引用

页码：857 / 879

页数：23

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