arXiv research

Paper provides criteria to detect non-admissible quandles via coloring.

This paper classifies all admissible quotients of a surface braid group up to order 127.

Spin Lefschetz fibrations can represent any group and lattice point.

Stability in homology of moduli spaces of admissible covers.

Torsion-free connections on $G$-structures are proven for certain groups.

Study of wild mapping class groups on complex reflection groups.

Study homogeneous Lorentzian manifolds under reductive Lie groups, reducing descriptions to semisimple groups.

New Lagrangian and special Lagrangian examples found in complex space.

3-manifold groups' word problem solved in nearly linear time.

When assessing group solvency, an important question is to what extent intragroup transfers may be considered, as this determines to which extent diversification can be achieved. We suggest a framework to describe the families of admissible transfers that range from the free movement of capital to excluding any transac…

Loxodromic elements are pseudo-Anosov on specific graphs.

Let $\A$ be a line arrangement in the complex projective plane $\PP^2$. Denote by $M$ its complement and by $\M$ the set of points in $\A$ with multiplicity at least 3. A rank one local system $\mathcal{L}$ on $M$ is admissible if roughly speaking the dimension of the cohomology groups $H^m(M,\mathcal{L})$ can be compu…

Study surfaces with free product fundamental groups, proving existence and properties.

Study geodesic orbit property on pseudo-Riemannian H-type nilmanifolds.

Embeddings preserve stable commutator length for surfaces.

Recently two search algorithms, A* and breadth-first branch and bound (BFBnB), were developed based on a simple admissible heuristic for learning Bayesian network structures that optimize a scoring function. The heuristic represents a relaxation of the learning problem such that each variable chooses optimal parents in…

We study the topology of admissible-loop spaces on a step-two Carnot group G. We use a Morse-Bott theory argument to study the structure and the number of geodesics on G connecting the origin with a 'vertical' point (geodesics are critical points of the 'Energy' functional, defined on the loop space). These geodesics t…

Let $Γ$ be a relatively hyperbolic group and let $μ$ be an admissible symmetric finitely supported probability measure on $Γ$. We extend Floyd-Ancona type inequalities up to the spectral radius of $μ$. We then show that when the parabolic subgroups are virtually abelian, the Martin boundary of the induced random walk o…

Study Coxeter groups over fusion rings and their geometric realisations.

We prove that admissible functions for Fubini-Study metrics on the complex projective space $P_{m}C$, of complex dimension $m$, invariant by a convenient automorphisms group, are lower bounded by a function going to minus infinity on the boundary of usual charts of $P_{m}C$. A similar lower bound holds on some projecti…

We describe a class (called regular) of invariant generalized complex structures on a real semisimple Lie group G. The problem reduces to the description of admissible pairs (\gk, ω), where \gk is an appropriate regular subalgebra of the complex Lie algebra \gg^{C} associated to G and ωis a closed 2-form on \gk, such t…

Let (G) be a connected compact non-abelian Lie-group and (T) a maximal torus of (G). A torus manifold with (G)-action is defined to be a smooth connected closed oriented manifold of dimension (2\dim T) with an almost effective action of (G) such that (M^T\neq \emptyset). We show that if there is a torus manifold (M) wi…

Question 2.6 of Bestvina's Questions in Geometric Group Theory asks whether every pair of boundaries of a given CAT(0) group G is cell-like equivalent. The question was posed by Bestvina shortly after the discovery, by Croke and Kleiner, of a CAT(0) group that admits multiple boundaries. Previously, it had been observe…

Four geometries govern sequential and distribution-free inference.

v2: An additional assumption was added in Theorem 4.8. In order to show that a connected abelian group is admissible on the site of locally compact spaces we must in addition assume that it is locally topologically divisible. This condition is used in the proof of Lemma 4.62.

We give sufficient conditions on a function invariant under the action of an isometry group to be Branson's Q-curvature of a metric in a given conformal class, using the conformal GJMS operators.

The paper proves Mabuchi solitons and constants on Fano admissible manifolds.

Analytic torsion equals dynamical zeta function for certain bundles.

The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but non-linear and non-convex constraint. The main results of this paper are significan…

A Lie-admissible algebra gives by anticommutativity a Lie algebra. In this work we study remarkable classes of Lie-admissible algebras such as Vinberg, PreLie algebras. We compute the corresponding binary quadratic operads and study their Koszul duality. Considering Lie algebras as Lie-admissible algebras we can define…

We construct the Fukaya category of a surface with genus greater than one and compute its Grothendieck group. We consider here a topological variant, in which we disregard the area form and use instead an admissibility condition borrowed from Heegaard-Floer theory which ensures invariance under isotopy. We also study a…

We study a topological analogue of idèlic class field theory for 3-manifolds, in the spirit of arithmetic topology. We firstly introduce the notion of a very admissible link $\mathcal{K}$ in a 3-manifold $M$, which plays a role analogous to the set of primes of a number field. For such a pair $(M,\mathcal{K})$, we intr…

Paper proposes robust method to detect risk heterogeneity across ethnic groups.

Godin introduced the categories of open closed fat graphs $Fat^{oc}$ and admissible fat graphs $Fat^{ad}$ as models of the mapping class group of open closed cobordism. We use the contractibility of the arc complex to give a new proof of Godin's result that $Fat^{ad}$ is a model of the mapping class group of open-close…

Investigates admissible metrics on compact Kähler varieties and their stability.

We give a differential-geometric construction of Calabi-Yau fourfolds by the `doubling' method, which was introduced in \cite{DY14} to construct Calabi-Yau threefolds. We also give examples of Calabi-Yau fourfolds from toric Fano fourfolds. Ingredients in our construction are \emph{admissible pairs}, which were first d…

New pseudometrics defined on knot spaces based on curve thickness and length.

New examples show deletion type admissible pairs can be rigid under rational saturation.

Topological obstructions to admissibility in $σ_k$-Loewner--Nirenberg problem

The paper is a study of geodesic in two-dimensional pseudo-Riemannian metrics. Firstly, the local properties of geodesics in a neighborhood of generic parabolic points are investigated. The equation of the geodesic flow has singularities at such points that leads to a curious phenomenon: geodesics cannot pass through s…

We introduce Riemannian metrics of positive scalar curvature on manifolds with Baas-Sullivan singularities, prove a corresponding homology invariance principle and discuss admissible products. Using this theory we construct positive scalar curvature metrics on closed smooth manifolds of dimension at least five which ha…

Study Nijenhuis operators on homogeneous spaces related to C*-algebras.

Researchers compare two methods for handlebody constructions, finding they are related with a 'background charge'.

We define the slope of a colored link in an integral homology sphere, associated to admissible characters on the link group. Away from a certain singular locus, the slope is a rational function which can be regarded as a multivariate generalization of the Kojima--Yamasaki $η$-function. It is the ratio of two Conway pot…

Investigate local Lie group structure of bisections over compact manifolds

Central limit theorem for Green metrics on hyperbolic groups.

New neural network architectures use signed permutation representations for finite groups, improving performance.

Given a hyperbolic surface, the set of all closed geodesics whose length is minimal form a graph on the surface, in fact a so-called fat graph, which we call the systolic graph. We study which fat graphs are systolic graphs for some surface (we call these admissible). There is a natural necessary condition on such grap…