# The complex of partial bases for Fn and finite generation of the Torelli subgroup of Aut (Fn)

```@article{Day2010TheCO,
title={The complex of partial bases for Fn and finite generation of the Torelli subgroup of Aut (Fn)},
author={Matthew B. Day and Andrew Putman},
journal={Geometriae Dedicata},
year={2010},
volume={164},
pages={139-153}
}```
• Published 9 December 2010
• Mathematics
• Geometriae Dedicata
We study the complex of partial bases of a free group, which is an analogue for Aut(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 Aut(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 Aut(Fn) is finitely generated.
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