Sigma invariants of direct products of groups
Copyright policy )Sigma invariants of direct products of groups
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 F_n which are not of type \mathrm{FP}_{n + 1} .
- Binghamton University United States
- Goethe University Frankfurt Germany
Homological methods in group theory, Generators, relations, and presentations of groups, 20F38, Topological methods in group theory, 20F38; 20F69, product conjecture, 20F69, products of groups, Group Theory (math.GR), Eilenberg-Mac Lane spaces, finitely generated groups, geometric invariants, Bieri-Neumann-Strebel invariants, Thompson group \(F\), groups of type \(\text{FP}_n\), FOS: Mathematics, homological invariants, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Geometric group theory, Mathematics - Group Theory, homotopical invariants
Homological methods in group theory, Generators, relations, and presentations of groups, 20F38, Topological methods in group theory, 20F38; 20F69, product conjecture, 20F69, products of groups, Group Theory (math.GR), Eilenberg-Mac Lane spaces, finitely generated groups, geometric invariants, Bieri-Neumann-Strebel invariants, Thompson group \(F\), groups of type \(\text{FP}_n\), FOS: Mathematics, homological invariants, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Geometric group theory, Mathematics - Group Theory, homotopical invariants
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