A generating function for the Euler characteristic of \(Out(F_ n)\)

DOI10.1016/0022-4049(87)90036-3zbMath0616.20009OpenAlexW1989739484WikidataQ115031756 ScholiaQ115031756MaRDI QIDQ1821195

Karen Vogtmann, John Smillie

Publication date: 1987

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(87)90036-3

zbMATH Keywords

free grouphomology groupsouter automorphismshomological finiteness conditionsrational Euler characteristictorsion-free subgroup of finite index

Mathematics Subject Classification ID

Homological methods in group theory (20J05) Automorphism groups of groups (20F28) Free nonabelian groups (20E05)

Related Items (17)

The topology and geometry of automorphism groups of free groups ⋮ On a theorem of Kontsevich ⋮ The integral cohomology of \(\text{Out}_ +(F_ 3)\) ⋮ Automorphisms of graphs, p-subgroups of \(Out(F_ n)\) and the Euler characteristic of \(Out(F_ n)\) ⋮ The contraction category of graphs ⋮ Homology of holomorphs of free groups. ⋮ Characteristic classes of moduli spaces— Riemann surface, graph, homology cobordism ⋮ The Euler characteristic of out \((F_n)\) ⋮ Multiple edges in M. Kontsevich's graph complexes and computations of the dimensions and Euler characteristics ⋮ Dimension of the Torelli group for \(\text{Out}(F_n)\). ⋮ Automorphisms of groups ⋮ Cohomology of \(\Aut(F_n)\) in the \(p\)-rank two case ⋮ Integral Euler Characteristic of OutF₁₁ ⋮ On the \(p\)-primary cohomology of \(\text{Out}(F_n)\) in the \(p\)-rank one case ⋮ The Euler characteristic of the Whitehead automorphism group of a free product ⋮ The symmetries of outer space. ⋮ Contractibility of fixed point sets of auter space

Cites Work

• Moduli of graphs and automorphisms of free groups
• Automorphisms of graphs, p-subgroups of \(Out(F_ n)\) and the Euler characteristic of \(Out(F_ n)\)
• The Euler characteristic of the moduli space of curves
• A Gauss-Bonnet formula for discrete arithmetically defined groups
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