arXiv research

Surgery paths in sphere graph have limited distance.

For a fully irreducible automorphism φof the free group F_k we compute the asymptotics of the intersection number n \mapsto i(T,T'φ^n) for trees T,T' in Outer space. We also obtain qualitative information about the geometry of the Guirardel core for the trees T and T'φ^n for n large.

New perspective on Heegaard splittings using square complexes and combinatorial measurements.

Paper unifies and simplifies proof of free product conditions.

Outer automorphism groups of Coxeter groups are trivial except for small ranks.

One of the most useful tools for studying the geometry of the mapping class group has been the subsurface projections of Masur and Minsky. Here we propose an analogue for the study of the geometry of Out(F_n) called submanifold projection. We use the doubled handlebody M_n = #^n S^2 \times S^1 as a geometric model of F…

We quantitatively relate the Patterson-Sullivant currents and generic stretching factors for free group automorphisms to the asymmetric Lipschitz metric on Outer space and to Guirardel's intersection number.

Following the approach of Dahmani, Guirardel and Osin, we extend the group theoretical Dehn filling theorem to show that the pre-images of infinite order elements have a certain structure of a free product. We then apply this result to show that groups hyperbolic relative to residually finite groups satisfying the Farr…

We prove that non-elementary hyperbolic groups grow exponentially more quickly than their infinite index quasiconvex subgroups. The proof uses the classical tools of automatic structures and Perron-Frobenius theory. We also extend the main result to relatively hyperbolic groups and cubulated groups. These extensions us…

Introduces a theorem for groups acting on trees.

New normal subgroups found in mapping class groups.

Study Poisson boundaries of building lattices and generalize rigidity results.

The paper shows symmetries of a geometric space for Coxeter groups.

We show that any infinite order element $g$ of a virtually cyclic hyperbolically embedded subgroup of a group $G$ is Morse, that is to say any quasi-geodesic connecting points in the cyclic group $C$ generated by $g$ stays close to $C$. This answers a question of Dahmani-Guirardel-Osin. What is more, we show that hyper…

We generalise the Karrass-Pietrowski-Solitar and the Nielsen realisation theorems from the setting of free groups to that of free products. As a result, we obtain a fixed point theorem for finite groups of outer automorphisms acting on the relative free splitting complex of Handel--Mosher and on the outer space of a fr…

Let $T$ be an $\mathbb{R}$-tree, equipped with a very small action of the rank $n$ free group $F_n$, and let $H \leq F_n$ be finitely generated. We consider the case where the action $F_n \curvearrowright T$ is indecomposable--this is a strong mixing property introduced by Guirardel. In this case, we show that the acti…

The paper shows how contracting elements in groups lead to large quotients with specific growth rates.

We prove that any action of a higher rank lattice on a Gromov-hyperbolic space is elementary. More precisely, it is either elliptic or parabolic. This is a large generalization of the fact that any action of a higher rank lattice on a tree has a fixed point. A consequence is that any quasi-action of a higher rank latti…

This paper establishes an equivalence between transitive double Lie algebroids and core diagrams.

The main result of this paper is that given a group $G$ acting geometrically by isometries on a CAT(0) space $X$ and a cyclic subgroup $H$ of $G$ generated by a rank-1 isometry of $X$, $H$ has bounded packing in $G$. We give two proofs of this result. The first one is by a characterization of rank-$1$ isometries by Ham…

Recovering core nodes in hypergraphs from fringe interactions.

Study reveals multiple core-periphery structures in interbank markets, transforming during financial crises.

New peripheral structure for core groups detects noninvertible knots.

AL$\ell_0$CORE tensor decomposition reduces computational cost for sparse count data.

We introduce the notion of the visual core of a hyperbolic 3-manifold N and explore its basic properties. The visual core can be thought of as a harmonic analysis analogue of the convex core. We investigate circumstances in which the visual core of a cover N' of N embeds under the covering map from N' to N. We apply th…

New combinatorial structures represent subgroups of surface groups, analogous to Stallings core graphs.

Paper introduces a core-periphery model for identifying informative network structures.

Publish a core-set of data to protect against adversarial use.

Estimates covariance matrices for matrix-variate data via core covariance geometry.

The paper extends quasimorphisms on subgroups to larger groups.

Probabilistic programming aids in automatically dating ice cores, reducing manual error and uncertainty.

Parallelizes word2vec for multi-core and many-core architectures.

Classifies stability of flat-core $p$-elasticae pinned at boundaries.

Study shows the volume of convex core for once-punctured torus groups is close to a fixed value.

The term "CoRE kernel" stands for correlation-resemblance kernel. In many applications (e.g., vision), the data are often high-dimensional, sparse, and non-binary. We propose two types of (nonlinear) CoRE kernels for non-binary sparse data and demonstrate the effectiveness of the new kernels through a classification ex…

New algorithm detects cores in graphs with community structure, improving vertex selection for better clustering.

We obtain upper and lower bounds on the difference between the renormalized volume and the volume of the convex core of a convex cocompact hyperbolic 3-manifold which depend on the injectivity radius of the boundary of the universal cover of the convex core and the Euler characteristic of the boundary of the convex cor…

Deep learning predicts nuclear equation of state from rotating core collapse GW signals.

This study examines cores within superclusters, highlighting their transitional nature and dynamical state.

The study allows for connected sums in manifolds with positive intermediate Ricci curvature.

Study signatures of torus links and their cores using Neumann's equivariant signatures and Hirzebruch's formula.

Proves NP and co-NP status for knot core recognition in solid torus.

Recovering core nodes from graph data with missing fringe interactions.

Core groups are link invariants defined by arc or region presentations.

Empty core found in max-loss non-centroid clustering.

We show that in any triangulation of a solid torus, there is a pre-core curve that lies in the 2-skeleton and that intersects the interior of each face in at most 10 straight arcs. By definition, a pre-core curve is a simple closed curve that becomes a core curve when a collar is attached to the boundary of the solid t…

CORe uses randomization to explore bandit problems without external noise.

Introduces Levi core for CR manifolds, linking it to global invariants.