Geodesic
Subgroups of direct products of limit groups
Martin R. Bridson1 ; James Howie2 ; Charles F. Miller III3 ; Hamish Short4
1 Mathematical Institute<br/>24-29 St Giles’<br/>Oxford OX1 3LB<br/>United Kingdom
2 Department of Mathematics and Maxwell Institute for Mathematical Sciences<br/>Heriot-Watt University<br/>Edinburgh EH14 4AS<br/>United Kingdom
3 Department of Mathematics and Statistics<br/>University of Melbourne<br/>Melbourne 3010<br/>Australia
4 L.A.T.P., U.M.R. 6632<br/>Centre de Mathématiques et d’Informatique<br/>39 Rue Joliot-Curie<br/>Université de Provence<br/>13453 Marseille cedex 13<br/>France
Annals of mathematics, Tome 170 (2009) no. 3, pp. 1447-1467

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SelaIf

$\Gamma_1,\dots,\Gamma_n$
are limit groups and
$S\subset\Gamma_1\times\dots\times\Gamma_n$
is of type
${\rm FP}_n(\mathbb Q)$
then
$S$
contains a subgroup of finite index that is itself a direct product of at most
$n$
limit groups. This answers a question of Sela.

DOI : 10.4007/annals.2009.170.1447

Martin R. Bridson 1 ; James Howie 2 ; Charles F. Miller III 3 ; Hamish Short 4

1 Mathematical Institute<br/>24-29 St Giles’<br/>Oxford OX1 3LB<br/>United Kingdom
2 Department of Mathematics and Maxwell Institute for Mathematical Sciences<br/>Heriot-Watt University<br/>Edinburgh EH14 4AS<br/>United Kingdom
3 Department of Mathematics and Statistics<br/>University of Melbourne<br/>Melbourne 3010<br/>Australia
4 L.A.T.P., U.M.R. 6632<br/>Centre de Mathématiques et d’Informatique<br/>39 Rue Joliot-Curie<br/>Université de Provence<br/>13453 Marseille cedex 13<br/>France 
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Martin R. Bridson; James Howie; Charles F. Miller III; Hamish Short. Subgroups of direct products of limit groups. Annals of mathematics, Tome 170 (2009) no. 3, pp. 1447-1467. doi: 10.4007/annals.2009.170.1447

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