Quasi-BNS invariants

2022/10/19 by Nicolaus Heuer, Dawid Kielak, Heuer, Nicolaus +1
Mathematics · #20F65 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2210.10607

openalex publication_date 2022/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of quasi-BNS invariants, where we replace homomorphism to \mathbb R by homogenous quasimorphisms to \mathbb R in the theory of Bieri-Neumann-Strebel invariants. We prove that the quasi-BNS invariant QΣ(G) of a finitely generated group G is open; we connect it to approximate finite generation of almost kernels of homogenous quasimorphisms; finally we prove a Sikorav-style theorem connecting QΣ(G) to the vanishing of the suitably defined Novikov homology.

Related

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