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.
Generalizes Dolbeault cohomology computation to Levi-flat CR structures on compact Lie groups.
No exact G₂-structures on compact Lie group quotients.
Proves cohomology of elliptic structures on Lie groups can be algebraic.
Compact complex manifolds with specific group actions are conformally flat.
Researchers compute cohomology of Lie groups using Lie algebras.
Compact groups with polynomial growth have specific embeddings.
New complex structures found on tangent bundles of Lie groups.
Characterizes isolated compact subgroups in Lie groups.
Non-invariant complex structures on Lie groups are not biholomorphic to invariant ones.
We introduce the group-compact coarse structure on a Hausdorff topological group in the context of coarse structures on an abstract group which are compatible with the group operations. We develop asymptotic dimension theory for the group-compact coarse structure generalizing several familiar results for discrete group…
We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also prove a related structure theorem for locally compact contractive local groups whic…
We describe simply connected compact exceptional simple Lie groups in very elementary way. We first construct all simply connected compact exceptional Lie groups G concretely. Next, we find all involutive automorphisms of G, and determine the group structures of the fixed points subgroup. They correspond to the classif…
Classifies Spin(7) structures on compact 8-manifolds with abelian fundamental group.
Study Weyl-Einstein structures on conformal solvmanifolds, proving Einstein property and classifying metrics.
We expose a K-theoretic approach to study group C*-algebras and C*-algebraic compact quantum groups: 1. The conception of multidimensional geometric quantization and the index of group C*-algebras; 2. the entire homology of noncommutative de Rham currents and the noncommutative Chern characters, and their computation f…
Explicitly describes pluriclosed metrics on compact Lie groups.
The paper explores -Kähler structures on Lie group quotients.
Found a new compact G2-structure on a 7-manifold.
We present some examples of locally conformal symplectic structures of the first kind on compact nilmanifolds which do not admit Vaisman metrics. One of these examples does not admit locally conformal Kähler metrics and all the structures come from left-invariant locally conformal symplectic structures on the correspon…
In this note we classify all homogeneous spaces admitting a -invariant -structure, assuming that is a compact Lie group and acts effectively on . They include a subclass of all homogeneous spaces with a -invariant -structure, where is a compact Lie group. There are ma…
We study spin structures on compact simply-connected homogeneous pseudo-Riemannian manifolds (M = G/H, g) of a compact semisimple Lie group G. We classify flag manifolds F = G/H of a compact simple Lie group which are spin. This yields also the classification of all flag manifolds carrying an invariant metaplectic stru…
We give a construction of integrable complex structures on the total space of a smooth principal bundle over a complex manifold, with an even dimensional compact Lie group as structure group, under certain conditions. This generalizes the constructions of complex structure on compact Lie groups by Samelson and Wang, an…
No left-invariant hypercomplex structures found on compact Lie groups.
We construct a smooth Lie group structure on the group of real analytic diffeomorphisms of a compact analytic manifold with corners. This generalises the known analogous results in the situation where the real analytic manifold has no corners. Additionally our approach uses a different construction.
Investigate local Lie group structure of bisections over compact manifolds
We study Lie group structures on groups of the form C^\infty(M,K)}, where M is a non-compact smooth manifold and K is a, possibly infinite-dimensional, Lie group. First we prove that there is at most one Lie group structure with Lie algebra C^\infty(M,k) for which the evaluation map is smooth. We then prove the existen…
We use the theory of dual of Fréchet-Schwartz (DFS) spaces to establish a sufficient condition for top-degree solvability for the differential complex associated to a hypocomplex locally integrable structure. As an application, we show that the top-degree cohomology of left-invariant hypocomplex structures on a compact…
Study compact symplectic solvmanifolds' hard Lefschetz property.
The paper explores automorphism groups of parabolic structures on aspherical manifolds.
Balanced metrics found on Lie groups and their quotients.
In this survey, we discuss a series of linearization problems--for Poisson structures, Lie algebroids, and Lie groupoids. The last problem involves a conjecture on the structure of proper groupoids. Attempting to prove this by the method of averaging leads to problems concerning almost actions of compact groups and alm…
In this paper we show as main results two structure theorems of a compact homogeneous locally conformally Kaehler (or shortly l.c.K.) manifold, a holomorphic structure theorem asserting that it has a structure of holomorphic principal fiber bundle over a flag manifold with fiber a 1-dimensional complex torus, and a met…
In this work, we describe how to obtain the structure of an infinite-dimensional Lie group on the group of compactly carried bundle automorphisms Autc(P) for a locally convex prinicpal bundle P over a finite-dimensional smooth sigma-compact base M. This is a generalization of previous work by Wockel, where the base M w…
Develops scalar curvature in generalized Kahler geometry and shows constant scalar curvature on compact Lie groups.
Classifies 3D manifolds with specific structures and automorphisms.
Study shows compact Sasakian manifolds are locally Heisenberg up to deformation.
We obtain a complete classification of hypercomplex manifolds, on which a compact group of automorphisms acts transitively. The description of the spaces as well as the proofs of our results use only the structure theory of reductive groups, in particular the notion of "stem" of a reduced root system, introduced in the…
Study on invariant anti-quasi-Sasakian structures on compact manifolds.
A Z-structure on a group G, defined by M. Bestvina, is a pair (\hat{X}, Z) of spaces such that \hat{X} is a compact ER, Z is a Z-set in \hat{X}, G acts properly and cocompactly on X=\hat{X}\Z, and the collection of translates of any compact set in X forms a null sequence in \hat{X}. It is natural to ask whether a given…
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 …
We generalise Atiyah and Hirzebruch's vanishing theorem for actions by compact groups on compact Spin-manifolds to possibly noncompact groups acting properly and cocompactly on possibly noncompact Spin-manifolds. As corollaries, we obtain some vanishing results for -type genera.
The paper explores SKT, balanced, and generalized Kähler structures on specific Lie groups.
We study the automorphism group of a compact 7-manifold endowed with a closed non-parallel G-structure, showing that its identity component is abelian with dimension bounded by min. This implies the non-existence of compact homogeneous manifolds endowed with an invariant closed non-parallel G-…
We study the action of the group of contact diffeomorphisms on CR deformations of compact three-dimensional CR manifolds. Using anisotropic function spaces and an anisotropic structure on the space of contact diffeomorphisms, we establish the existence of local transverse slices to the action of the contact diffeomorph…
Study groups with polynomial growth, finding structure and applications.
Paper proves metrics of positive Ricci curvature on fiber bundles.
It was shown by Samelson and Wang that each compact Lie group K of even dimension admits left-invariant complex structures. When K has odd dimension it admits a left-invariant CR-structure of maximal dimension. This has been proved recently by Charbonnel and Khalgui who have also given a complete algebraic description …
We present some basic results on a natural Poisson structure on any compact symmetric space. The symplectic leaves of this structure are related to the orbits of the corresponding real semisimple group on the complex flag manifold.