%0 Generic %1 Day2010 %A Day, Matthew B. %A Putman, Andrew %D 2010 %K class mapping surfaces %T The complex of partial bases for F_n and finite generation of the Torelli subgroup of Aut(F_n) %U http://arxiv.org/abs/1012.1914 %X We study the complex of partial bases of a free group, which is an analogue for $\Aut(F_n)$ 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 $\Aut(F_n)$ is highly connected. Using these results, we give a new, topological proof of a theorem of Magnus that asserts that the Torelli subgroup of $\Aut(F_n)$ is finitely generated.

@misc{Day2010, abstract = { We study the complex of partial bases of a free group, which is an analogue for $\Aut(F_n)$ 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 $\Aut(F_n)$ is highly connected. Using these results, we give a new, topological proof of a theorem of Magnus that asserts that the Torelli subgroup of $\Aut(F_n)$ is finitely generated. }, added-at = {2010-12-12T07:49:39.000+0100}, author = {Day, Matthew B. and Putman, Andrew}, biburl = {https://www.bibsonomy.org/bibtex/2b397fa44232b8e984d8b1ec583d5d01e/uludag}, description = {The complex of partial bases for F_n and finite generation of the Torelli subgroup of Aut(F_n)}, interhash = {e843d98b847380f876918c4cfc79a3f6}, intrahash = {b397fa44232b8e984d8b1ec583d5d01e}, keywords = {class mapping surfaces}, note = {cite arxiv:1012.1914 Comment: 15 pages}, timestamp = {2010-12-12T07:49:40.000+0100}, title = {The complex of partial bases for F_n and finite generation of the Torelli subgroup of Aut(F_n)}, url = {http://arxiv.org/abs/1012.1914}, year = 2010 }