arXiv research

Study shows quotient group is infinitely generated.

Reductive quotients preserve klt singularities in algebraic geometry.

The study examines the smoothness of submetries in Riemannian manifolds.

Study of Dehn filling quotients in hierarchically hyperbolic groups.

Geodesics spiral around compact subsets in CAT(0) spaces.

Paper solves Hessian quotient equations in Lorentz-Minkowski space with Dirichlet boundary conditions.

This paper investigates which smooth manifolds arise as quotients (orbit spaces) of flows of vector fields. Such quotient maps were already known to be surjective on fundamental groups, but this paper shows that every epimorphism of countably presented groups is induced by the quotient map of some flow, and that higher…

Compact quotients of homogeneous spaces are studied, leading to new findings about sphere bundles.

New manifold types defined on quotient spaces.

We consider quotients of spheres by linear actions of real tori. To each quotient we associate a matroid built out of a diagonalization of the torus action. We find the integral homology groups of the resulting quotient spaces in terms of the Tutte polynomial of the matroid. We also find the homotopy type and homology …

A classification result for Ricci-flat anti-self-dual asymptotically locally Euclidean 4-manifolds is obtained: they are either hyperkähler (one of the gravitational instantons classified by Kronheimer), or they are a cyclic quotient of a Gibbons-Hawking space. The possible quotients are described in terms of the monop…

Rational ellipticity proven for $G$-manifolds with specific quotient properties.

Paper solves curvature equations in Minkowski space for non-convex domains.

New insights into ends of quotient spaces and graphs.

Study non-existence of complex ball quotients in Torelli locus.

Study shows infinitely many metrics with nonnegative sectional or positive Ricci curvature on specific 5D quotients.

We study the hypersymplectic spaces obtained as quotients of flat hypersymplectic space R^{4d} by the action of a compact Abelian group. These 4n-dimensional quotients carry a multi-Hamilitonian action of an n-torus. The image of the hypersymplectic moment map for this torus action may be described by a configuration o…

Defines hypercomplex analytic spaces and schemes.

Study involutions on 3D small covers, proving quotient spaces are linked 2-spheres.

Study shows infinitely many nonnegatively curved metrics on quotient spaces.

The paper establishes Pogorelov type estimates for solutions to Hessian quotient equations in hyperbolic space.

We derive a necessary and sufficient condition for the existence of symmetric space structures on quotients of Banach symmetric spaces. Along the way, we investigate the different kinds of reflection subspaces and their Lie triple systems.

New method uses quotient predictor space for better PAC-Bayes bounds, reducing KL divergence and improving model performance.

By means of cohomology groups, we study relationships between equivariant gerbes with connection over a manifold with a Lie group action and gerbes with connection over the quotient space.

We investigate relation between Dehn fillings and commensurability of hyperbolic 3-manifolds. The set consisting of the commensurability classes of hyperbolic 3-manifolds admits the quotient topology induced by the geometric topology. We show that this quotient space satisfies some separation axioms. Roughly speaking, …

The paper explores conditions for topological rigidity in quotients of the Davis complex.

Decouples homotopy quotients of generalised configuration spaces on surfaces.

We study an integration theory in circle equivariant cohomology in order to prove a theorem relating the cohomology ring of a hyperkahler quotient to the cohomology ring of the quotient by a maximal abelian subgroup, analogous to a theorem of Martin for symplectic quotients. We discuss applications of this theorem to q…

The study shows a finite number of groups acting on hyperbolic spaces with bounded entropy and compact quotient.

Indecomposable symmetric Lorentzian manifolds of non-constant curvature are called Cahen-Wallach spaces. Their isometry classes are described by continuous families of real parameters. We derive necessary and sufficient conditions for the existence of compact quotients of Cahen-Wallach spaces in terms of these paramete…

The paper characterizes unit balls among Stein spaces with specific groups using Bergman-Einstein metrics.

This article studies the volume of compact quotients of reductive homogeneous spaces. Let $G/H$ be a reductive homogeneous space and $Γ$ a discrete subgroup of $G$ acting properly discontinuously and cocompactly on $G/H$. We prove that the volume of $Γ\backslash G/H$ is the integral, over a certain homology class of $Γ…

Polynomial density theorem for specific subgroup orbits in quotient spaces.

New insights into a complex hyperbolic braid group quotient.

Study cohomology of ball quotients and their compactifications.

If a Lie group acts on a manifold freely and properly, pulling back by the quotient map gives an isomorphism between the differential forms on the quotient manifold and the basic differential forms upstairs. We show that this result remains true for actions that are not necessarily free nor proper, as long as the ident…

New spherical Milnor spaces for diffeological groups with geometric and topological properties.

We study some cases when the sectional curvature remains positive under the taking of quotients by certain nonfree isometric actions of Lie groups. We consider the actions of the groups $S^1$ and $S^3$ such that the quotient space can be endowed with a smooth structure using the fibrations $S^3/S^1{\simeq}S^2$ and $S^7…

This paper studies the canonical Chow quotient of a smooth projective variety by a reductive algebraic group. The main purpose is to give some topological interpretations and characterization of Chow quotient which have the advantage to be more intuitive and geometric. This is to be done over the field of complex numbe…

We prove estimates for the sectional curvature of hyperkaehler quotients and give applications to moduli spaces of solutions to Nahm's equations and Hitchin's equations.

The article characterizes complex torus quotients with numerical conditions.

This article discusses the existence problem of a compact quotient of a symmetric space by a properly discontinuous group with emphasis on the non-Riemannian case. Discontinuous groups are not always abundant in a homogeneous space $G/H$ if $H$ is non-compact. The first half of the article elucidates general machinery …

Given a metric space $X$ and a function $f: X \to \mathbb{R}$, the Reeb construction gives metric a space $X_f$ together with a quotient map $X \to X_f$. Under suitable conditions $X_f$ becomes a metric graph and can therefore be used as a graph approximation to $X$. The Gromov-Hausdorff distance from $X_f$ to $X$ is b…

We characterize finite groups G generated by orthogonal transformations in a finite-dimensional Euclidean space V whose fixed point subspace has codimension one or two in terms of the corresponding quotient space V/G with its quotient piecewise linear structure.

A result of Jost and Zuo is used to show that for a large class of finite-dimensional hyperkähler quotients, the only L2 harmonic forms lie in the middle dimension, and are of type (k,k) with respect to all complex structures. The argument is extended to some moduli spaces which appear as infinite-dimensional quotients…

Starting from the recent classification of quotients of Freund--Rubin backgrounds in string theory of the type AdS_{p+1} x S^q by one-parameter subgroups of isometries, we investigate the physical interpretation of the associated quotients by discrete cyclic subgroups. We establish which quotients have well-behaved cau…

Study shows nontrivial intersections of subgroups on homogeneous spaces.

Complex projective varieties are quotients of polydiscs under specific group actions.