arXiv research

The study examines groups with a specific automorphism property using BNS-invariant.

In 1987 Bieri, Neumann and Strebel introduced a geometric invariant for discrete groups. In this article we compute and explicitly describe the BNS-invariant for the pure braid groups.

Study BNS invariants to prove algebraic fibrations of certain groups.

The BNS invariant is applied to Kähler groups in new proofs and results.

We describe the BNS invariant of Kaehler groups. As an application we prove that if the fundamental group of a Kaehler manifold is solvable, it is virtually nilpotent.

We investigate Friedl-Lück's universal $L^2$-torsion for descending HNN extensions of finitely generated free groups, and so in particular for $F_n$-by-$\mathbb{Z}$ groups. This invariant induces a semi-norm on the first cohomology of the group which is an analogue of the Thurston norm for $3$-manifold groups. We prove…

We study the Newton polytopes of determinants of square matrices defined over rings of twisted Laurent polynomials. We prove that such Newton polytopes are single polytopes (rather than formal differences of two polytopes); this result can be seen as analogous to the fact that determinants of matrices over commutative …

Any endomorphism of a finitely generated free group naturally descends to an injective endomorphism of its stable quotient. In this paper, we prove a geometric incarnation of this phenomenon: namely, that every expanding irreducible train track map inducing an endomorphism of the fundamental group gives rise to an expa…

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

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…

The paper shows how certain Kähler groups are uniquely determined by their profinite completions.

In this article we develop the theory of residually finite rationally $p$ (RFR$p$) groups, where $p$ is a prime. We first prove a series of results about the structure of finitely generated RFR$p$ groups (either for a single prime $p$, or for infinitely many primes), including torsion-freeness, a Tits alternative, and …

Graphs with specific spanning trees yield RAAGs, with applications to BBGs.

Consider a group G and an epimorphism u_0:G\to\Z inducing a splitting of G as a semidirect product ker(u_0)\rtimes_\varphi\Z with ker(u_0) a finitely generated free group and \varphi\in Out(ker(u_0)) representable by an expanding irreducible train track map. Building on our earlier work [Dynamics on free-by-cyclic grou…