More Like this

1. Relative cubulation of relative strict hyperbolization

   https://doi.org/10.1112/jlms.70093  

   Lafont, Jean‐François; Ruffoni, Lorenzo (April 2025, Journal of the London Mathematical Society)

   Abstract We prove that many relatively hyperbolic groups obtained by relative strict hyperbolization admit a cocompact action on a cubical complex. Under suitable assumptions on the peripheral subgroups, these groups are residually finite and even virtually special. We include some applications to the theory of manifolds, such as the construction of new non‐positively curved Riemannian manifolds with residually finite fundamental group, and the existence of non‐triangulable aspherical manifolds with virtually special fundamental group. 

   more » « less
2. Equivariant hierarchically hyperbolic structures for 3-manifold groups via quasimorphisms

   https://doi.org/10.5802/aif.3654  

   Hagen, Mark; Russell, Jacob; Sisto, Alessandro; Spriano, Davide (January 2025, Annales de l'Institut Fourier)

   Behrstock, Hagen and Sisto classified 3-manifold groups admitting a hierarchically hyperbolic space structure. However, these structures were not always equivariant with respect to the group. In this paper, we classify 3-manifold groups admitting equivariant hierarchically hyperbolic structures. The key component of our proof is that the admissible groups introduced by Croke and Kleiner always admit equivariant hierarchically hyperbolic structures. For non-geometric graph manifolds, this is contrary to a conjecture of Behrstock, Hagen and Sisto and also contrasts with results about CAT(0) cubical structures on these groups. Perhaps surprisingly, our arguments involve the construction of suitable quasimorphisms on the Seifert pieces, in order to construct actions on quasi-lines. 

   more » « less
3. Simple 𝑝-adic Lie groups with abelian Lie algebras

   https://doi.org/10.1515/crelle-2024-0030  

   Caprace, Pierre-Emmanuel; Minasyan, Ashot; Osin, Denis (June 2024, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract For each prime 𝑝 and each positive integer 𝑑, we construct the first examples of second countable, topologically simple 𝑝-adic Lie groups of dimension 𝑑 whose Lie algebras are abelian.This answers several questions of Glöckner and Caprace–Monod.The proof relies on a generalization of small cancellation methods that applies to central extensions of acylindrically hyperbolic groups. 

   more » « less
4. Special cubulation of strict hyperbolization

   https://doi.org/10.1007/s00222-024-01241-9  

   Lafont, Jean-François; Ruffoni, Lorenzo (June 2024, Inventiones mathematicae)

   Abstract We prove that the Gromov hyperbolic groups obtained by the strict hyperbolization procedure of Charney and Davis are virtually compact special, hence linear and residually finite. Our strategy consists in constructing an action of a hyperbolized group on a certain dual$$\operatorname {CAT}(0)$$ $CAT\left(0\right)$cubical complex. As a result, all the common applications of strict hyperbolization are shown to provide manifolds with virtually compact special fundamental group. In particular, we obtain examples of closed negatively curved Riemannian manifolds whose fundamental groups are linear and virtually algebraically fiber. 

   more » « less
5. High-resolution Observations of a Small-scale Cancellation Nanoflare: Supporting Evidence for the Cancellation Nanoflare Model

   https://doi.org/10.3847/2041-8213/adca3a  

   Tang, Zehao; Shen, Yuandeng; Zhou, Chengrui; Yao, Surui; Liu, Dongxu (May 2025, The Astrophysical Journal Letters)

   Abstract An analytical cancellation nanoflare model has recently been established to show the fundamental role that ubiquitous small-scale cancellation nanoflares play in solar atmospheric heating. Although this model is well supported by simulations, observational evidence is needed to deepen our understanding of cancellation nanoflares. We present observations of a small-scale cancellation nanoflare event, analyzing its magnetic topology evolution, triggers, and physical parameters. Using coordinated observations from the Solar Dynamics Observatory and Goode Solar Telescope, we identify a photospheric flow-driven cancellation event with a flux cancellation rate of ∼10¹⁵Mx s⁻¹and a heating rate of 8.7 × 10⁶erg cm⁻²s⁻¹. The event shows the characteristic transition fromπ-shaped to X-shaped magnetic configuration before the formation of a 2″ current sheet, closely matching model predictions. This event provides critical observational support for the cancellation nanoflare model and its role in solar atmospheric heating. 

   more » « less