Quasi-BNS invariants

Nicolaus Heuer; Dawid Kielak

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arXiv · 2210.10607

Quasi-BNS invariants

Nicolaus Heuer·Dawid Kielak

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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 $Q\Sigma(G)$ 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 $Q\Sigma(G)$ to the vanishing of the suitably defined Novikov homology.

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BibTeX RIS

Nicolaus Heuer, Dawid Kielak. 2022-10-19. Quasi-BNS invariants. https://arxiv.org/abs/2210.10607

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