The complex of partial bases for Fn and finite generation of the Torelli subgroup of Aut(Fn)
Abstract
We study the complex of partial bases of a free group, which is an analogue for (Fn) of the curve complex for the mapping class group. We prove that it is connected and simply connected, and we also prove that its quotient by the Torelli subgroup of (Fn) is highly connected. Using these results, we give a new, topological proof of a theorem of Magnus that asserts that the Torelli subgroup of (Fn) is finitely generated.
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