New proof shows 4-manifolds can't support complex structures.
problem Proving 4-manifolds can't support complex structures.
method New proof of complex structure non-existence for real-hyperbolic 4-manifolds.
result Extended graph 4-manifolds with positive Euler characteristic cannot support a complex structure.
Study characteristic classes for TC structures on principal G-bundles.
problem Classifying principal G-bundles with TC structures.
method Algebraic-geometric construction using power maps on BcomG. result Construction of characteristic classes for TC structures on SU(n), U(n), and Sp(n) bundles. New framework for interpretable firm characteristics factors.
problem Creating statistically efficient and economically interpretable factors from firm characteristics.
method Grouping related characteristics and deriving one factor per group, combining economic intuition with data-driven clustering.
result Parsimonious, transparent factors outperform benchmarks in out-of-sample tests.
What are called secondary characteristic classes in Chern-Weil theory are a refinement of ordinary characteristic classes of principal bundles from cohomology to differential cohomology. We consider the problem of refining the construction of secondary characteristic classes from cohomology sets to cocycle spaces; and …
The paper develops a theory of Ehresmann structures in positive characteristic.
problem Developing a theory for Ehresmann structures in positive characteristic.
method Comparing Frobenius-Ehresmann structures with Cartan geometries and studying their equivalence.
result Formulating and proving the Ehresmann-Weil-Thurston principle for Frobenius-Ehresmann structures.
Sheng and Zuo's characteristic forms are invariants of a variation of Hodge structure. We show that they characterize Gross's canonical variations of Hodge structure of Calabi-Yau type over (Hermitian symmetric) tube domains.
The paper localizes an index and provides a condition for the orientability of a monopole moduli space.
problem Localization of a KO∗(extpt)-valued index and orientability of the Pin−(2) monopole moduli space. method Introducing G±(n,s+,s−) structures and formulating characteristic submanifolds for these structures. result The KO∗(pt)-valued index is localized to the characteristic submanifold, and a condition for the moduli space to be orientable is provided. New Euler characteristics for groupoids generalize orbifold Euler characteristics.
problem Generalizing orbifold Euler characteristics to non-orbifold groupoids.
method Introducing two Euler characteristics for groupoids, using o-minimal structures, and relating them to orbifold Euler characteristics.
result The two new Euler characteristics coincide and generalize orbifold Euler characteristics.
The paper defines and calculates Euler characteristics for quandles.
problem Defining and calculating Euler characteristics for quandles.
method Definition and calculation of Euler characteristics for quandles.
result The quandle Euler characteristic of a compact connected Riemannian symmetric space coincides with the topological Euler characteristic.
An almost contact metric structure is parametrized by a section of an associated homogeneous fibre bundle, and conditions for this to be a harmonic section, and a harmonic map, are studied. These involve the characteristic vector field, and the almost complex structure in the contact subbundle. Several examples are giv…
This paper describes the characteristic group of LCP structures and their construction.
problem Understanding the characteristic group of LCP structures and their construction.
method Analyzing the characteristic group and constructing LCP structures.
result It is possible to endow certain quotients with LCP structures.
We call two Engel structures isotopic if they are homotopic through Engel structures by a homotopy that fixes the characteristic line field. In the present paper we define an isotopy invariant of Engel structures on oriented circle bundles over closed oriented three-manifolds and apply it to give an isotopy classificat…
This paper formalizes manifolds in positive characteristic varieties.
problem Establishing l-adic formal manifold structures on positive characteristic varieties.
method Develops and proves the existence of l-adic formal manifold structures and abelianized Galois symmetries.
result Proves l-adic homotopic equivalence and l-local lifting for simply-connected varieties.
Study compatible and associated metrics for contact-symplectic structures, showing geodesic integral curves and minimal leaf properties.
problem Characteristics foliations of metric contact-symplectic structures.
method Analysis of compatible and associated metrics, study of geodesic integral curves, and minimal leaf properties.
result Integral curves of the Reeb vector field are geodesics for any compatible metric, and associated metrics share a common volume element.
Two types of 4-manifolds disagree on minimum Euler characteristic.
problem Disagreement between topological and smooth 4-manifolds.
method Comparison of topological and smooth 4-manifolds with a fixed fundamental group.
result Minimum Euler characteristic differs between topological and smooth 4-manifolds.
New operator reveals unique features of sl(N) link homology.
problem Understanding unique features of sl(N) link homology.
method Constructing an operator on sl(N) link homology with mod N coefficients.
result Structural features of sl(P) link homology are revealed.
It is well known that a foliation F of a smooth manifold M gives rise to a rich cohomological theory, its characteristic (i.e., leafwise) cohomology. Characteristic cohomologies of F may be interpreted, to some extent, as functions on the space P of integral manifolds (of any dimension) of the characteristic distributi…
Survey on Nambu-Poisson structures in infinite dimensions.
problem Generalization of Poisson and Nambu-Poisson structures in infinite dimensions.
method Study properties of associated characteristic distribution and projective/direct limits.
result Properties and limits of Nambu-Poisson structures in convenient setting.
The study connects conic connections and torsion-free principal connections on G-structures.
problem Relating torsion tensors of principal connections to characteristic conic connections.
method Formulating and verifying conditions for the existence of characteristic conic connections implying torsion-free principal connections.
result Conditions for the existence of characteristic conic connections imply the existence of torsion-free principal connections, verified for adjoint varieties of simple Lie algebras.
Engel structures on M x S^1 and M x I are studied in this paper, where M is a 3-dimensional manifold. We suppose that these structures have characteristic line fields parallel to the fibres, S^1 or I. It is proved that they are characterized by contact structures on the cross section M, the twisting numbers, and Legend…
It is well-known that 7-dimensional 3-Sasakian manifolds carry a one-parametric family of compatible G_2 structures and that they do not admit a characteristic connection. In this note, we show that there is nevertheless a distinguished cocalibrated G_2 structure in this family whose characteristic connection along wit…
This paper extends geometric structure theory to infinite type structures.
problem Calculating characteristic class relations in complex Cartan geometries.
method Improves representation theory for infinite type structures.
result Direct calculation of characteristic class relations from structure group representation.
Develops Chern-Weil theory for singular foliations.
problem Chern-Weil theory for Haefliger-singular foliations.
method Constructs explicit forms representing characteristic classes in de Rham cohomology.
result Theory applies to general smooth Haefliger structures up to homotopy.
We introduce characteristics into chromatic homotopy theory. This parallels the prime characteristics in number theory as well as in our earlier work on structured ring spectra and unoriented bordism theory. Here, the K(n)-local Hopkins-Miller classes ζn take the places of the prime numbers, and this allows us to di…
The paper extends a conjecture about Euler characteristics of perverse sheaves on certain Kähler manifolds.
problem The conjecture about Euler characteristics of perverse sheaves on compact aspherical Kähler manifolds.
method The method involves expressing the Euler characteristic as an intersection number involving the characteristic cycle, and using curvature conditions to deduce non-negativity. For the second result, the local system is shown to underlie a complex variation of Hodge structures, leading to the desired inequality from curvature properties of the period map.
result The conjecture holds for compact aspherical Kähler manifolds with non-positive holomorphic bisectional curvature and for projective manifolds with a faithful semi-simple rigid local system.
The present article investigates Sp(3) structures on 14-dimensional Riemannian manifolds, a continuation of the recent study of manifolds modeled on rank two symmetric spaces (here: SU(6)/Sp(3)). We derive topological criteria for the existence of such a structure and construct large families of homogeneous examples. A…
This paper shows the reduced characteristic group of Lie LCP manifolds is simply connected.
problem Understanding the structure of Lie LCP manifolds and their characteristic groups.
method Restricting the action of the fundamental group to the non-flat factor of the universal cover and taking the connected component of the identity in the closure of this restriction.
result The reduced characteristic group of any Lie LCP manifold is simply connected.
New invariants detect exotic smooth structures in 4-manifolds.
problem Detect exotic smooth structures in 4-manifolds using invariants of 2-handlebodies.
method Investigates invariants of 4-dimensional 2-handlebodies from the Temperley-Lieb category in positive characteristic.
result Height n=2 invariant vanishes on CP2, CP2, and S2imesS2 for p>3. The infinitesimal period relation (also known as Griffiths' transversality) is the system of partial differential equations constraining variations of Hodge structure. This paper presents a study of the characteristic cohomology associated with that system of pde.
We classify 7-dimensional cocalibrated $\G_2$-manifolds with parallel characteristic torsion and non-abelian holonomy. All these spaces admit a metric connection ∇c with totally skew-symmetric torsion and a spinor field Ψ1 solving the equations in the common sector of type II superstring theory. T…
CCVAE captures label characteristics in VAEs for better representation learning.
problem Capturing rich label characteristics in VAEs without conflating them with label values.
method Developed CCVAE, a novel VAE model that explicitly captures label characteristics in latent space.
result CCVAE allows for effective and general interventions like smooth traversals and diverse conditional generation.
Paper characterizes foliated bundle classes via quasi-morphisms and studies their boundedness.
problem Characterizing bounded characteristic classes of foliated bundles.
method Using non-descendible quasi-morphisms on the universal covering of the structure group.
result Non-existence of foliated structures on some Hamiltonian fibrations and non-triviality of the second bounded cohomology group.
The paper conjectures a 4D characterization of tight contact structures and proves it for certain cases.
problem Characterizing tight contact structures in 4D.
method Analyzing slice-Bennequin inequalities and Ozsváth-Szabó contact invariants.
result Affirmative answers to conjectures about tight contact structures in 4D.
On an orientable manifold M, we consider a regular even dimensional foliation F which is globally defined by a set of k-independent 1-forms. We give necessary and sufficient conditions for the existence of a regular Poisson structure on M whose Characteristic foliation is precisely F. Moreover, introducing a special cl…
New surgery method for foliated spheres preserves key numbers.
problem Creating groups from foliated sphere concordance classes.
method Define surgery procedure, find obstruction, use surgery to preserve characteristic numbers.
result Groups structure on concordance classes of foliated spheres.
The article studies conic connections on complex manifolds and their geometric properties.
problem Characterizing and understanding conic connections on complex manifolds.
method Develops a new approach to the cubic torsion and studies the geometric conditions for its vanishing.
result Provides a geometric condition characterizing the vanishing of cubic torsion.
The paper studies complex curves with translation structures from differential equations.
problem Analyzing the structure of complex curves from differential equations.
method Defined isoresidual fibration and computed characteristics of complex curves.
result Determined Euler characteristic and classified connected components of isoresidual fibers.
We study the characteristic foliation of a twisted Jacobi manifold. We show that a twisted Jacobi manifold is foliated into leaves that are, according to the parity of the dimension, endowed with a twisted contact or a twisted locally conformal symplectic structure.
In this note we prove that every non characteristically filiform Lie algebra is endowed with an affine structure.
This study links blockchain design to cryptos' distributional characteristics.
problem Understanding the relationship between blockchain design and cryptos' distributional characteristics.
method Used spectral clustering to cluster cryptos based on their blockchain mechanisms and operational features.
result Clusters of cryptos share similar blockchain mechanisms, supporting the hypothesis.
We show that φ-invariant submanifolds of metric contact pairs with orthogonal characteristic foliations make constant angles with the Reeb vector fields. Our main result is that for the normal case such submanifolds of dimension at least 2 are all minimal. We prove that an odd-dimensional φ-invariant submanifold …
Develops relative cohomology for Lie groupoids and algebroids.
problem Lack of relative cohomology theory in Lie groupoids and algebroids.
method Structural theory development, van Est maps relation, intrinsic characteristic classes definition.
result Provides an intrinsic definition of characteristic classes using relative cohomology.
Review and generalize Haefliger's differentiable cohomology for diffeomorphisms and flat Cartan groupoids.
problem Define and investigate differentiable cohomology for diffeomorphisms and flat Cartan groupoids.
method Define Haefliger's differentiable cohomology for diffeomorphisms, investigate its structure, and generalize to flat Cartan groupoids.
result Define characteristic maps for geometric structures on manifolds associated to flat Cartan groupoids.
New Euler characteristic and Burnside group defined for definable groupoids.
problem Defining Euler characteristics and Burnside groups for a broad class of groupoids.
method Introducing universal Euler characteristic and Burnside group for orbit spaces of definable groupoids.
result Every invariant of orbit space definable groupoids arises as a homomorphism of the universal Euler characteristic.
Kontsevich's classes distinguish smooth structures on fiber bundles.
problem Distinguishing smooth structures on fiber bundles.
method Using Kontsevich's characteristic classes and real blow-up construction.
result Kontsevich's classes are determined by the topology of the 2-point configuration space bundle.
We prove some general results about the relation between the 1-cocycles of an arbitrary Lie algebroid A over M and the leaves of the Lie algebroid foliation on M associated with A. Using these results, we show that a E1(M)-Dirac structure L induces on every leaf F of its characteristic foliation a…
We prove the vanishing of a certain characteristic class of flat vector bundles when the structure groups of the bundles are contained in GL(N,Z). We do so by explicitly writing the characteristic class as an exact form on the base of the bundle.
Study cohomotopy classes for 4-manifolds using complex spin structures.
problem Understanding cohomotopy classes for families of 4-manifolds with complex spin structures.
method Using Bauer--Furuta invariants in parametrised stable homotopy theory.
result Definition of characteristic cohomotopy classes on Thom spectra.