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The complex of partial bases for F n and finite generation of the Torelli subgroup of Aut (F n )

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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.

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Authors and Affiliations

  1. Department of Mathematics 253-37, California Institute of Technology, Pasadena, CA, 91125, USA

    Matthew Day

  2. Department of Mathematics, Rice University, MS 136, 6100 Main St., Houston, TX, 77005, USA

    Andrew Putman

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  1. Matthew Day
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  2. Andrew Putman
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Correspondence to Andrew Putman.

Additional information

Matthew Day: Supported in part by an NSF postdoctoral fellowship.

Andrew Putman: Supported in part by NSF grant DMS-1005318.

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Day, M., Putman, A. The complex of partial bases for F n and finite generation of the Torelli subgroup of Aut (F n ). Geom Dedicata 164, 139–153 (2013). https://doi.org/10.1007/s10711-012-9765-6

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