Stable homology of automorphism groups of free groups

• 成果类型: Article
• 署名作者: Galatius, Soren
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.173.2.3
• 发表日期: 2011
• 页码: 705-768
• 关键词: mapping class-groups; finite subsets; Homotopy; SPACES; STABILITY; SURFACES; fibrations; category; graphs; MODULI

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.