Dimension of the Torelli group for Out(Fn)

• 成果类型: Article
• 署名作者: Bestvina, Mladen; Bux, Kai-Uwe; Margalit, Dan
• 署名单位: Utah System of Higher Education; University of Utah; University of Virginia
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-007-0055-0
• 发表日期: 2007
• 页码: 1-32
• 关键词: automorphisms; genus-2; graphs

摘要

Let T-n be the kernel of the natural map Out( F-n). GL(n)( Z). We use combinatorial Morse theory to prove that Tn has an Eilenberg-MacLane space which is ( 2n - 4)- dimensional and that H2n-4( T-n, Z) is not finitely generated ( n >= 3). In particular, this shows that the cohomological dimension of Tn is equal to 2n-4 and recovers the result of Krstic-McCool that T-3 is not finitely presented. We also give a new proof of the fact, due to Magnus, that T-n is finitely generated.