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Daniel T. Wise

Publications and source records attributed to Daniel T. Wise.

At least 19 recordsLinked to original sources
arXiv2026

On the spectral radius of the non-backtracking matrix of the configuration model

We prove a concentration result for the leading eigenvalue of the non--backtracking matrix of the configuration model under the assumption of uniformly bounded degrees. Let $P$ denote the limiting degree distribution. Assuming polynomial approximation, we show that as the number of vertices tends to infinity, the leading eigenvalue of the non--backtracking matrix concentrates around \[ \frac{\mathbb{E}[P(P-1)]}{\mathbb{E}[P]}. \] This quantity corresponds to the mean offspring number of the excess--degree branching process associated with the local limit of the configuration model. As a byproduct of our work we explain how this result can be applied to prove the density of the growth rates of the subgroups of the free group.

math.GR↗
arXiv2026

On the growth spectrum of hyperbolic groups

We study the growth spectrum of groups acting on hyperbolic spaces, i.e.\ the set of exponential growth rates achieved by subgroups. For a finitely generated free group or a surface group acting convex-cocompactly on a proper geodesic hyperbolic metric space, we prove that the growth spectrum is the full interval $[0, ω_G]$. For any hyperbolic group, we prove that the growth spectrum contains a large interval $[0, ω_{\mathcal{F}}]$ where $ω_{\mathcal{F}} \geq ω_G / 2$, with strict inequality when the action is divergent. In the case of the Cayley graph of a free group, we also present an approach via the non-backtracking matrix of the configuration model, connecting the density of growth rates to a spectral concentration result for random graphs.

math.GR↗
arXiv2025

Strict C(6) complexes

We define strict C(n) small-cancellation complexes, intermediate to C(n) and C(n+1), and we prove groups acting properly cocompactly on a simply-connected strict C(6) complex are hyperbolic relative to a collection of maximal virtually free abelian subgroups of rank 2. We study geometric walls in a simply-connected strict C(6) complex, and we use them to prove a convex cocompact (cosparse) core theorem for (relatively) quasiconvex subgroups of strict C(6) groups. We provide an examples showing the convex cocompact core theorem is false without the strict C(6) assumption.

math.GR↗
arXiv2024

The Hrushovski Property for Compact Special Cube Complexes

We show that any compact nonpositively curved cube complex $Y$ embeds in a compact nonpositively curved cube complex $R$ where each combinatorial injective partial local isometry of $Y$ extends to an automorphism of $R$. When $Y$ is special and the collection of injective partial local isometries satisfies certain conditions, we show that $R$ can be chosen to be special and the embedding $Y\hookrightarrow R$ can be chosen to be a local isometry.

math.GN↗
arXiv2024

Hyperbolicity in non-metric cubical small-cancellation

Given a non-positively curved cube complex $X$, we prove that the quotient of $π_1X$ defined by a cubical presentation $\langle X\mid Y_1,\dots, Y_s\rangle$ satisfying sufficient non-metric cubical small-cancellation conditions is hyperbolic provided that $π_1X$ is hyperbolic. This generalises the fact that finitely presented classical $C(7)$ small-cancellation groups are hyperbolic.

math.GR↗
arXiv2023

Cubulating random quotients of hyperbolic cubulated groups

We show that low-density random quotients of cubulated hyperbolic groups are again cubulated (and hyperbolic). Ingredients of the proof include cubical small-cancellation theory, the exponential growth of conjugacy classes, and the statement that hyperplane stabilizers grow exponentially more slowly than the ambient cubical group.

math.GR↗
arXiv2023

Negative Immersions and Finite Height Mappings

Given a monomorphism $Ψ:\mathcal{H}\rightarrow \mathcal{F}$ where $\mathcal{H}$ is a proper free factor of the free group $\mathcal{F}$, we show the associated mapping torus $X$ of $Ψ$ has negative immersions iff $\mathcal{H}$ has finite height in $π_1X$ iff $Ψ$ is fully irreducible. We survey related properties and discuss possible directions to pursue further.

math.GR↗
arXiv2023

Nonpositive Towers in Bing's Neighbourhood

Every 2-dimensional spine of an aspherical 3-manifold has the nonpositive towers property, but every collapsed 2-dimensional spine of a 3-ball containing a 2-cell has an immersed sphere.

math.GT↗
arXiv2022

Cubulating Small Cancellation Free Products

We give a simplified approach to the cubulation of small-cancellation quotients of free products of cubulated groups. We construct fundamental groups of compact nonpositively curved cube complexes that do not virtually split.

math.GR↗
arXiv2022

Failure of the finitely generated intersection property for ascending HNN extensions of free groups

The main result in this paper is the failure of the finitely generated intersection property (FGIP) of ascending HNN extensions of non-cyclic finite rank free groups. This class of group consists of free-by-cyclic groups and properly ascending HNN extensions of free groups. We also give a sufficient condition for the failure of the FGIP in the context of relative hyperbolicity, we apply this to free-by-cyclic groups of exponential growth.

math.GR↗
arXiv2021

Local Quasiconvexity of Groups acting on Small Cancellation Complexes

Given a group acting cellularly and cocompactly on a simply-connected 2-complex, we provide a criterion establishing that all finitely generated subgroups have quasiconvex orbits. This work generalizes the "perimeter method". As an application, we show that high-powered one-relator products $A \ast B / \nclose{r^n}$ are coherent if $A$ and $B$ are coherent.

math.GR↗