A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper classifies fibrations of 3-dimensional flat orbifolds.
This paper classifies fibrations of flat orbifolds, advancing flat 4-manifold classification.
Study of flat metrics on orbifolds and their moduli spaces.
This article is devoted to a study of flat orbifold vector bundles. We construct a bijection between the isomorphic classes of proper flat orbifold vector bundles and the equivalence classes of representations of the orbifold fundamental groups of base orbifolds. We establish a Bismut-Zhang like anomaly formula for the…
Proves orbifold singularities for Ricci-flat metrics on certain Kähler varieties.
Study flat manifolds' collapsed limits as flat orbifolds.
We provide an algebraic description of the Teichmüller space and moduli space of flat metrics on a closed manifold or orbifold and study its boundary, which consists of (isometry classes of) flat orbifolds to which the original object may collapse. It is also shown that every closed flat orbifold can be obtained by col…
In this paper, we establish an equality between the analytic torsion introduced by Dar\cite{MR876230} and the orbifold analytic torsion defined by Ma \cite{MR2140438} on a compact manifold with isolated conical singularities which in addition has an orbifold structure. We assume the orbifold flat vector bundle is an ho…
Study on counting flat connections over -orbifolds, proving moduli space compact and smooth.
Study shows dynamics of rank 1 orbifolds in flat surfaces.
The paper characterizes Eguchi-Hanson space and its higher-dimensional analogs using Lichnerowicz Laplacian.
The paper constructs flat metrics on orbifolds and resolutions.
We show that all closed flat n-manifolds are diffeomorphic to a cusp cross-section in a finite volume hyperbolic (n+1)-orbifold.
Study on energy of maps from K3 surface to flat orbifold.
Study on harmonic forms on K3 surfaces converging to a flat 4D orbifold.
Let G be an n-dimensional crystallographic group (n-space group). If G is a Z-reducible, then the flat n-orbifold E^n/G has a nontrivial fibered orbifold structure. We prove that this structure can be described by a generalized Calabi construction, that is, E^n/G is represented as the quotient of the Cartesian product …
In this article we verify an orbifold version of a conjecture of Nimershiem from 1998. Namely, for every flat -manifold , we show that the set of similarity classes of flat metrics on which occur as a cusp cross-section of a hyperbolic -orbifold is dense in the space of similarity classes of flat metri…
The paper classifies and proves properties of ALE manifolds and orbifolds.
We present explicit constructions of complete Ricci-flat Kahler metrics that are asymptotic to cones over non-regular Sasaki-Einstein manifolds. The metrics are constructed from a complete Kahler-Einstein manifold (V,g_V) of positive Ricci curvature and admit a Hamiltonian two-form of order two. We obtain Ricci-flat Ka…
We prove that any asymptotically locally Euclidean scalar-flat Kähler 4-orbifold whose isometry group contains a 2-torus is isometric, up to an orbifold covering, to a quaternionic-complex quotient of a -dimensional quaternionic vector space by a -torus. In order to do so, we first prove that any compact anti…
Study of orbifold Chern character using superconnections.
We give a classification of toric anti-self-dual conformal structures on compact 4-orbifolds with positive Euler characteristic. Our proof is twistor theoretic: the interaction between the complex torus orbits in the twistor space and the twistor lines induces meromorphic data, which we use to recover the conformal str…
The paper classifies 4D Ricci-flat ALE manifolds and their properties.
New obstructions found for smooth desingularization of compact Einstein orbifolds.
For X = R, C, or H it is well known that cusp cross-sections of finite volume X-hyperbolic (n+1)-orbifolds are flat n-orbifolds or almost flat orbifolds modelled on the (2n+1)-dimensional Heisenberg group N_{2n+1} or the (4n+3)-dimensional quaternionic Heisenberg group N_{4n+3}(H). We give a necessary and sufficient co…
New Ricci flows found with Einstein orbifolds at infinity.
Blowing up flat metrics yields balanced ones with constant curvature.
In this paper we describe the classification of all the geometric fibrations of a closed flat Riemannian 4-manifold over a 1-orbifold.
The article studies Ricci-flat metrics on complex projective space.
This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such compactness for spaces of Bach-flat (for example half-conformally flat) metrics …
Study of ALF manifolds via hyperkahler quotients of affine spaces.
Study Higgs bundles and flat connections on quasi-regular Sasakian manifolds.
The paper studies the topology and geometry of simple orbifolds, generalizing concepts from simple polytopes.
We determine that the deformation space of convex real projective structures, that is, projectively flat torsion-free connections with the geodesic convexity property on a compact 2-orbifold of negative Euler characteristic is homeomorphic to a cell of certain dimension. The basic techniques are from Thurston's lecture…
The paper studies Ricci flow with specific curvature and volume constraints, proving convergence and curvature bounds.
We construct bi-Lipschitz embeddings into Euclidean space for manifolds and orbifolds of bounded diameter and curvature. The distortion and dimension of such embeddings is bounded by diameter, curvature and dimension alone. Our results also apply for bounded subsets of complete Riemannian manifolds, and complete flat a…
We give a purely geometrical smooth characterization of closed infrasolv manifolds and orbifolds by showing that, up to diffeomorphism, these are precisely the spaces which admit a collapse with bounded curvature and diameter to compact flat orbifolds. Moreover, we distinguish irreducible smooth fake tori geometrically…
We show that any asymptotically locally Euclidean (ALE) metric which is obstruction-flat or extended obstruction-flat must be ALE of a certain optimal order. Moreover, our proof applies to very general elliptic systems and in any dimension . The proof is based on the technique of Cheeger-Tian for Ricci-flat m…
Unified theory of orbifolds and cohomology.
In this paper we introduce the concept of Deligne cohomology of an orbifold. We prove that the third Deligne cohomology group of a smooth étale groupoid classify gerbes with connection over the groupoid. We argue that the -field and the discrete torsion in type II superstring theories are special kinds of gerbes wit…
Study closed G2-structures with T3-symmetry, classifying them into types and deriving hypersymplectic structures.
New -instantons constructed on Joyce's manifold.
The study of flat manifolds and their reducible holonomy groups.
The paper defines curvature at infinity for flat manifolds.
Simply connected moduli space of Ricci flat metrics on K3 surfaces.
Let be a finite group and $\Y$ a -gerbe over an orbifold $\B$. A disconnected orbifold $\hat{\Y}$ and a flat U(1)-gerbe on $\hat{\Y}$ is canonically constructed from $\Y$. Motivated by a proposal in physics, we study a mathematical duality between the geometry of the -gerbe $\Y$ and the geometry of $\hat{…
We study Chern-Simons theory on 3-manifolds M that are circle-bundles over 2-dimensional orbifolds S by the method of Abelianisation. This method, which completely sidesteps the issue of having to integrate over the moduli space of non-Abelian flat connections, reduces the complete partition function of the non-Abelian…
We construct new explicit toric scalar-flat K{ä}hler ALE metrics on weighted projective spaces of non-compact type, which we use to obtain smooth extremal K{ä}hler metrics on appropriate resolutions of orbifolds. In particular, we obtain new extremal metrics certain resolutions of weighted projective spaces of compact …