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On the Bieri–Neumann–Strebel–Renz invariants of residually free groups

Part of: Connections with homological algebra and category theory

Published online by Cambridge University Press:  21 July 2020

Dessislava H. Kochloukova  and
Francismar Ferreira Lima
Dessislava H. Kochloukova
Affiliation:
State University of Campinas, São Paulo, Brazil (desi@ime.unicamp.br)
Francismar Ferreira Lima
Affiliation:
Federal University of Technology, Paraná, Brazil (francismarf@utfpr.edu.br)
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Abstract

We calculate the Bieri–Neumann–Strebel–Renz invariant Σ1(G) for finitely presented residually free groups G and show that its complement in the character sphere S(G) is a finite union of finite intersections of closed sub-spheres in S(G). Furthermore, we find some restrictions on the higher-dimensional homological invariants Σn(G, ℤ) and show for the discrete points Σ2(G)dis, Σ2(G, ℤ)dis and Σ2(G, ℚ)dis in Σ2(G), Σ2(G, ℤ) and Σ2(G, ℚ) that we have the equality Σ2(G)dis = Σ2(G, ℤ)dis = Σ2(G, ℚ)dis.

Keywords

homological finiteness properties of groupsresidually free groups

MSC classification

Primary: 20J05: Homological methods in group theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 3 , August 2020 , pp. 807 - 829
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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