Stable homology of automorphism groups of free groups

被引：46

作者：

Galatius, Soren ^{[1
]}

机构：

[1] Stanford Univ, Stanford, CA 94305 USA

来源：

ANNALS OF MATHEMATICS | 2011年 / 173卷 / 02期

基金：

美国国家科学基金会;

关键词：

MAPPING CLASS-GROUPS; FINITE SUBSETS; HOMOTOPY; SPACES; STABILITY; SURFACES; FIBRATIONS; CATEGORY; GRAPHS; MODULI;

D O I：

10.4007/annals.2011.173.2.3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Homology of the group Aut(F-n) of automorphisms of a free group on n generators is known to be independent of n in a certain stable range. Using tools from homotopy theory, we prove that in this range it agrees with homology of symmetric groups. In particular we confirm the conjecture that stable rational homology of Aut(F-n) vanishes.

引用

页码：705 / 768

页数：64

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