The Product Conjecture for the homological Bieri–Neumann–Strebel–Renz invariants is proved over a field. Under certain hypotheses the Product Conjecture is shown to also hold over Z, even though D. Schütz has recently shown that the Conjecture is false in general over Z. Our version over Z is applied in a joint paper with D. Kochloukova [5] to show that for all n Thompson’s group F contains subgroups of type Fn which are not of type FPn + 1.
Classification :
20-XX, 55-XX, 00-XX
Mots-clés :
Bieri–Neumann–Strebel invariants, product conjecture, products of groups
Affiliations des auteurs :
Robert Bieri
1
;
Ross Geoghegan
2
1
Johann Wolfgang Goethe-Universität, Frankfurt am Main, Germany
2
Binghamton University, USA
Robert Bieri; Ross Geoghegan. Sigma invariants of direct products of groups. Groups, geometry, and dynamics, Tome 4 (2010) no. 2, pp. 251-261. doi: 10.4171/ggd/82
@article{10_4171_ggd_82,
author = {Robert Bieri and Ross Geoghegan},
title = {Sigma invariants of direct products of groups},
journal = {Groups, geometry, and dynamics},
pages = {251--261},
year = {2010},
volume = {4},
number = {2},
doi = {10.4171/ggd/82},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/82/}
}
TY - JOUR
AU - Robert Bieri
AU - Ross Geoghegan
TI - Sigma invariants of direct products of groups
JO - Groups, geometry, and dynamics
PY - 2010
SP - 251
EP - 261
VL - 4
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/82/
DO - 10.4171/ggd/82
ID - 10_4171_ggd_82
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%A Ross Geoghegan
%T Sigma invariants of direct products of groups
%J Groups, geometry, and dynamics
%D 2010
%P 251-261
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%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/82/
%R 10.4171/ggd/82
%F 10_4171_ggd_82
