Dimension of the Torelli group for Out(Fn)
Mladen Bestvina, Kai-Uwe Bux, Dan Margalit
Abstract
Let Tn be the kernel of the natural map from Out(Fn) to 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(Tn,Z) is not finitely generated (n at least 3). In particular, this recovers the result of Krstic-McCool that T3 is not finitely presented. We also give a new proof of the fact, due to Magnus, that Tn is finitely generated.
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