arXiv research

Regular subgroups of SL3(R) are identified and ruled out.

Classifies isotopy classes of links from Thompson's group F and its subgroup.

We prove a Morse Lemma for coarsely regular quasigeodesics in nonpositively curved symmetric spaces and euclidean buildings X. The main application is a simpler coarse geometric characterization of Morse subgroups of the isometry groups Isom(X) as undistorted subgroups which are coarsely uniformly regular. We show furt…

Exponential growth of stable subgroups in Morse geodesics.

This paper classifies regular maps with Euler characteristic -p^4 for a prime p≥5.

Study slice-regular polynomial functions via twistor space group actions.

Let G/H be a strongly regular homogeneous space such that H is a Lie group of inner type. We show that G/H admits a proper action of a discrete non-virtually abelian subgroup of G if and only if G/H admits a proper action of a subgroup L of G locally isomorphic to SL(2,R). We classify all such spaces.

We show that two uniform lattices of a regular right-angled Fuchsian building are commensurable, provided the chamber is a polygon with at least six edges. We show that in an arbitrary Gromov-hyperbolic regular right-angled building associated to a graph product of finite groups, a uniform lattice is commensurable with…

GAME improves matrix completion by considering subgroup-specific latent structures.

Study Einstein Lie groups and geodesic orbit manifolds, finding some are not geodesic orbit.

Model patching closes subgroup performance gaps in skin cancer classification.

New method identifies subgroups in censored data.

New subgroup found in Lie groups with unusual properties.

We study Veech groups of covering surfaces of primitive translation surfaces. Therefore we define congruence subgroups in Veech groups of primitive translation surfaces using their action on the homology with entries in $\mathbb{Z}/a\mathbb{Z}$. We introduce a congruence level definition and a property of a primitive t…

In this paper it is proven that if the group of covering translations of the covering space of a compact, connected, $P^2$-irreducible 3-manifold corresponding to a non-trivial, finitely-generated subgroup of its fundamental group is infinite, then either the covering space is almost compact or the subgroup is infinite…

Selective regression allows abstention to improve fairness criteria.

New framework tackles stochastic latent subgroup heterogeneity in online decision-making.

We study cocompact lattices with dense projections in a product $G_1 \times G_2$ of locally compact groups and show, under the assumption that each $G_i$ is a closed subgroup of the automorphism group $Aut(T_i)$ of a regular tree satisfying certain local transitivity conditions, that such a lattice is contained in only…

Smooth knots in complex hyperbolic plane limit sets to chains or R-circles.

We study the set of critical exponents of discrete groups acting on regular trees. We prove that for every real number $δ$ between $0$ and $\frac{1}{2}\log q$, there is a discrete subgroup $Γ$ acting without inversion on a $(q+1)$-regular tree whose critical exponent is equal to $δ$. Explicit construction of edge-index…

Let G be a finitely presented group. Scott and Swarup have constructed a canonical splitting of G which encloses all almost invariant sets over virtually polycyclic subgroups of a given length. We give an alternative construction of this regular neighbourhood, by showing that it is the tree of cylinders of a JSJ splitt…

Study on Borel Anosov subgroups in SL(d,R) for d≠5,8k±1.

We show that for groups acting acylindrically on simplicial trees the $K$- and $L$-theoretic Farrell-Jones Conjecture relative to the family of subgroups consisting of virtually cyclic subgroups and all subconjugates of vertex stabilisers holds. As an application, for amalgamated free products acting acylindrically on …

We give a geometric interpretation of the maximal Satake compactification of symmetric spaces $X=G/K$ of noncompact type, showing that it arises by attaching the horofunction boundary for a suitable $G$-invariant Finsler metric on $X$. As an application, we establish the existence of natural bordifications, as orbifold…

We consider invariant Riemannian metrics on compact homogeneous spaces G/H where an intermediate subgroup K between G and H exists, so that the homogeneous space G/H is the total space of a Riemannian submersion. We study the question as to whether enlarging the fibers of the submersion by a constant scaling factor ret…

The Cayley graph of quandles reveals structural properties and is studied for various classes.

Constructs flows on quotients of Lie groups for Anosov subgroups.

Analogue of classical Hurwitz numbers is defined in the work for regular coverings of surfaces with marked points by seamed surfaces. Class of surfaces includes surfaces of any genus and orientability, with or without boundaries; coverings may have certain singularities over the boundary and marked points. Seamed surfa…

Anosov groups limit sets are Ahlfors regular, with applications in Teichmüller spaces.

The paper characterizes finite metacyclic subgroups in mapping class groups of surfaces.

Let $Γ$ be the fundamental group of a manifold modeled on three dimensional Sol geometry. We prove that $Γ$ has a finite index subgroup $G$ which has a rational growth series with respect to a natural generating set. We do this by enumerating $G$ by a regular language. However, in contrast to most earlier proofs of thi…

New findings on mapping class group actions on the circle, improving critical regularity.

The identification of predictive biomarkers from a large scale of covariates for subgroup analysis has attracted fundamental attention in medical research. In this article, we propose a generalized penalized regression method with a novel penalty function, for enforcing the hierarchy structure between the prognostic an…

This paper presents an original approach for jointly fitting survival times and classifying samples into subgroups. The Coxlogit model is a generalized linear model with a common set of selected features for both tasks. Survival times and class labels are here assumed to be conditioned by a common risk score which depe…

We introduce and study the notion of a chain group of homeomorphisms of a one-manifold, which is a certain generalization of Thompson's group $F$. The resulting class of groups exhibits a combination of uniformity and diversity. On the one hand, a chain group either has a simple commutator subgroup or the action of the…

We give a necessary and sufficient condition for orbits of commutative Hermann actions and actions of the direct product of two symmetric subgroups on compact Lie groups to be biharmonic in terms of symmetric triad with multiplicities. By this criterion, we determine all the proper biharmonic submanifolds in irreducibl…

We expand Topological Field Theory on some special CW-complexes (brane complexes). This Brane Topological Field Theory one-to-one corresponds to infinite dimensional Frobenius Algebras, graduated by CW-complexes of lesser dimension. We define general and regular Hurwitz numbers of brane complexes and prove that they ge…

For a pinched Hadamard manifold $X$ and a discrete group of isometries $Γ$ of $X$, the critical exponent $δ_Γ$ is the exponential growth rate of the orbit of a point in $X$ under the action of $Γ$. We show that the critical exponent for any family $\mathcal{N}$ of normal subgroups of $Γ_0$ has the same coarse behaviour…

Let X be a proper hyperbolic geodesic metric space and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G is not amenable then its second continuous bounded cohomology group with coefficients the regular representation does not vanish. This yields some structure results for such groups.

We prove the generalized Margulis lemma with a uniform index bound on an Alexandrov $n$-space $X$ with curvature bounded below, i.e., small loops at $p\in X$ generate a subgroup of the fundamental group of unit ball $B_1(p)$ that contains a nilpotent subgroup of index $\le w(n)$, where $w(n)$ is a constant depending on…

A fixed point theorem is proved for inverse transducers, leading to an automata-theoretic proof of the fixed point subgroup of an endomorphism of a finitely generated virtually free group being finitely generated. If the endomorphism is uniformly continuous for the hyperbolic metric, it is proved that the set of regula…

We introduce a coarse flow space for relatively hyperbolic groups and use it to verify a regularity condition for the action of relatively hyperbolic groups on their boundaries. As an application the Farrell-Jones Conjecture for relatively hyperbolic groups can be reduced to the peripheral subgroups (up to index 2 over…

We introduce a technique for proving quantitative representation stability theorems for sequences of representations of certain finite linear groups over a field of characteristic zero. In particular, we prove a vanishing result for higher syzygies of VIC- and SI-modules, which can be thought of as a weaker version of …

Let $\mathrm{Mod}(S_g)$ be the mapping class group of the closed orientable surface of genus $g \geq 1$. For $k \geq 2$, we consider the standard $k$-sheeted regular cover $p_k: S_{k(g-1)+1} \to S_g$, and analyze the liftable mapping class group $\mathrm{LMod}_{p_k}(S_g)$ associated with the cover $p_k$. In particular,…

Study on Hausdorff dimension of Anosov subgroup limit sets under specific affine complexity.

The paper proposes a method to identify subgroups with different treatment effects in time-to-event data.

We prove an explicit and sharp upper bound for the Castelnuovo-Mumford regularity of an FI-module V in terms of the degrees of its generators and relations. We use this to refine a result of Putman on the stability of homology of congruence subgroups, extending his theorem to previously excluded small characteristics a…

It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs us…