Sigma invariants of direct products of groups
Robert Bieri
Johann Wolfgang Goethe-Universität, Frankfurt am Main, GermanyRoss Geoghegan
Binghamton University, USA
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Abstract
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 , even though D. Schütz has recently shown that the Conjecture is false in general over . Our version over is applied in a joint paper with D. Kochloukova [5] to show that for all Thompson’s group contains subgroups of type which are not of type .
Cite this article
Robert Bieri, Ross Geoghegan, Sigma invariants of direct products of groups. Groups Geom. Dyn. 4 (2010), no. 2, pp. 251–261
DOI 10.4171/GGD/82