Dimension of the Torelli group for Out(Fn)
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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