arXiv research

Proves connection between $\ell^2$-Betti numbers and BNSR invariants.

Study investigates lattices fibring over the circle, focusing on BNSR invariants.

Researchers compute BNSR-invariants for surface Houghton groups.

The study bounds Dehn functions of coabelian subgroups using a second BNSR invariant.

Investigates BNSR invariants of link and knot groups, proving specific properties.

The paper shows BNSR-invariants of McCool groups are either dense or empty.

The BNSR-invariants of a group $G$ are a sequence $Σ^1(G)\supseteq Σ^2(G) \supseteq \cdots$ of geometric invariants that reveal important information about finiteness properties of certain subgroups of $G$. We consider the symmetric automorphism group $ΣAut_n$ and pure symmetric automorphism group $PΣAut_n$ of the free…

We give a complete computation of the BNSR-invariants $Σ^m(H_n)$ of the Houghton groups $H_n$. Partial results were previously obtained by the author, with a conjecture about the full picture, which we now confirm. The proof involves covering relevant subcomplexes of an associated $CAT(0)$ cube complex by their interse…

We inspect the BNSR-invariants $Σ^m(P_n)$ of the pure braid groups $P_n$, using Morse theory. The BNS-invariants $Σ^1(P_n)$ were previously computed by Koban, McCammond and Meier. We prove that for any $3\le m\le n$, the inclusion $Σ^{m-2}(P_n)\subseteq Σ^{m-3}(P_n)$ is proper, but $Σ^\infty(P_n)=Σ^{n-2}(P_n)$. We writ…

BNSR invariants are contained in the complement of tropical varieties.

Bieri, Geoghegan and Kochloukova computed the BNSR-invariants $Σ^m(F)$ of Thompson's group $F$ for all $m$. We recompute these using entirely geometric techniques, making use of the Stein--Farley CAT(0) cube complex on which $F$ acts.

Generalizes results on Bieri-Neumann-Strebel-Renz invariants and tropical varieties.

Complete description of BNSR invariants for Lodha-Moore groups, proving finiteness properties.

This paper stems from the observation (arising from work of T. Delzant) that "most" Kähler groups virtually algebraically fiber, i.e. admit a finite index subgroup that maps onto $\Bbb{Z}$ with finitely generated kernel. For the remaining ones, the Albanese dimension of all finite index subgroups is at most one, i.e. t…