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Inventiones mathematicae

, Volume 170, Issue 1, pp 1–32 | Cite as

Dimension of the Torelli group for Out(Fn)

  • Mladen Bestvina
  • Kai-Uwe Bux
  • Dan Margalit
Article

Abstract

Let \(\mathcal{T}_{n}\) be the kernel of the natural map Out(Fn)→GLn(ℤ). We use combinatorial Morse theory to prove that \(\mathcal{T}_{n}\) has an Eilenberg–MacLane space which is (2n-4)-dimensional and that \(H_{2n-4}(\mathcal{T}_{n},\mathbb{Z})\) is not finitely generated (n≥3). In particular, this shows that the cohomological dimension of \(\mathcal{T}_{n}\) is equal to 2n-4 and recovers the result of Krstić–McCool that \(\mathcal{T}_3\) is not finitely presented. We also give a new proof of the fact, due to Magnus, that \(\mathcal{T}_{n}\) is finitely generated.

Keywords

Homotopy Type Mapping Class Group Morse Function Label Graph Cohomological Dimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  2. 2.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

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