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.
Proves a vanishing property for symplectic manifold cohomology.
Study cohomological and metric properties of non-Kähler complex manifolds.
Study on properties of Oeljeklaus-Toma manifolds, including cohomology and metrics.
Property A was introduced by Yu as a non-equivariant analogue of amenability. Nigel Higson posed the question of whether there is a homological characterisation of property A. In this paper we answer Higson's question affirmatively by constructing analogues of group cohomology and bounded cohomology for a metric space …
We introduce a "qualitative property" for Bott-Chern cohomology of complex non-Kähler manifolds, which is motivated in view of the study of the algebraic structure of Bott-Chern cohomology. We prove that such a property characterizes the validity of the -Lemma. This follows from a quantitativ…
This survey summarizes the results discussed in a talk at "Bielefeld Geometry & Topology Days" held at Bielefeld University in July 2015. We are interested in quantitative and qualitative properties of Bott-Chern cohomology. We announce new results obtained in [D. Angella, N. Tardini, Quantitative and qualitative cohom…
While small deformations of Kähler manifolds are Kähler too, we prove that the cohomological property to be -pure-and-full is not a stable condition under small deformations. This property, that has been recently introduced and studied by T.-J. Li and W. Zhang in [Comparing tamed and compatible symp…
The abstract discusses p-harmonic forms and their geometric properties, proving new theorems about Lp-cohomology.
New proofs and refined theorems on bounded cohomology.
Study on deformations of Lie groupoid morphisms and their properties.
It is known that, for a regular riemannian foliation on a compact manifold, the properties of its basic cohomology (non-vanishing of the top-dimensional group and Poincaré Duality) and the tautness of the foliation are closely related. If we consider singular riemannian foliations, there is little or no relation betwee…
Proved Burghelea Conjecture for specific groups.
We study Bott-Chern and Aeppli cohomologies of a vector space endowed with two anti-commuting endomorphisms whose square is zero. In particular, we prove an inequality à la Frölicher relating the dimensions of the Bott-Chern and Aeppli cohomologies to the dimensions of the Dolbeault cohomologies. We prove that the equa…
In [1] it was shown that K^, a certain differential cohomology functor associated to complex K-theory, satisfies the Mayer-Vietoris property when the underlying manifold is compact. It turns out that this result is quite general. The work that follows shows the M-V property to hold on compact manifolds for any differen…
In [1] it was shown that K^, a certain differential cohomology functor associated to complex K-theory, satisfies the Mayer-Vietoris property when the underlying manifold is compact. It turns out that this result is quite general. The work that follows shows the M-V property to hold on compact manifolds for any differen…
Study cohomologies on manifolds with locally conformally symplectic structures.
New displacement technique vanishes bounded cohomology in all degrees.
Study on twisted Dolbeault cohomology in Kähler foliations.
In this paper we define a new cohomology of a smooth manifold called Lichnerowicz type cohomology attached to a function. Firstly, we study some basic properties of this cohomology as: a de Rham type isomorphism, dependence on the function, singular forms, relative cohomology, Mayer-Vietoris sequence, homotopy invarian…
Estimates Kaehler metrics' diameter in big cohomology classes.
The study examines Eschenburg orbifolds with positive sectional curvature and their geometric/topological properties.
Compact manifolds without odd cohomology have almost fixed points.
New cohomological invariants defined for foliations.
This study shows that certain cohomology groups of symplectic manifolds are always even-dimensional.
New computations show various properties of bounded cohomology in finitely presented groups.
Study on complex manifolds and their cohomology properties.
In this paper we give a new characterization of the h-vector of the chromatic polynomial of a graph. We introduce reduced chromatic cohomology of a graph and show that h_i are its Betti numbers. We then discuss various combinatorial properties of these cohomologies. In particular we prove that these cohomologies depend…
Classifies certain types of geometric shapes with specific algebraic properties.
Extends Hard Lefschetz Property to isometric flows and shows equivalence.
We provide further techniques to study the Dolbeault and Bott-Chern cohomologies of deformations of solvmanifolds by means of finite-dimensional complexes. By these techniques, we can compute the Dolbeault and Bott-Chern cohomologies of some complex solvmanifolds, and we also get explicit examples, showing in particula…
We prove properties of the Schweitzer complex and its cohomologies.
We extend Massey products from cohomology to differential cohomology via stacks, organizing and generalizing existing constructions in Deligne cohomology. We study the properties and show how they are related to more classical Massey products in de Rham, singular, and Deligne cohomology. The setting and the algebraic m…
Researchers twist Deligne cohomology for the first time.
Following T.-J. Li, W. Zhang [Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom.], we continue to study the link between the cohomology of an almost-complex manifold and its almost-complex structure. In particular, we apply the same argument in [T…
Extends Donaldson's techniques to symplectic orbifolds, proving existence of sections and computing cohomology.
The paper explores higher property T in lattices and its connections to geometric phenomena.
The paper extends Dolbeault cohomology to almost complex manifolds and provides new tools for studying their properties.
We prove the finiteness of the cohomology of torsion-free lattices in a semisimple Lie group of real rank one with coefficients in the distribution vector globalization of Harish-Chandra modules. The cohomology is expressed in terms of automorphic and cusp forms. We also consider the Lie-algebra cohomology of these glo…
We study the J-invariant and J-anti-invariant cohomological subgroups of the de Rham cohomology of a compact manifold M endowed with an almost-Kähler structure (J, ω, g). In particular, almost-Kähler manifolds satisfying a Lefschetz type property, and solvmanifolds endowed with left-invariant almost-complex structures …
In order to look for a well-behaved counterpart to Dolbeault cohomology in D-complex geometry, we study the de Rham cohomology of an almost D-complex manifold and its subgroups made up of the classes admitting invariant, respectively anti-invariant, representatives with respect to the almost D-complex structure, miming…
We study quasi-isometry invariants of Gromov hyperbolic spaces, focussing on the l_p-cohomology and closely related invariants such as the conformal dimension, combinatorial modulus, and the Combinatorial Loewner Property. We give new constructions of continuous l_p-cohomology, thereby obtaining information about the l…
The first cohomology of Poisson algebras is described and conditions for its vanishing are established.
Study on symplectic semi-characteristic using cohomology and vector fields.
Introduces a new periodic Deligne cohomology with twists by gerbes.
In this thesis, we study cohomological properties of non-Kähler manifolds. In particular, we are concerned in investigating the cohomology of compact (almost-)complex manifolds, and of manifolds endowed with special structures, e.g., symplectic structures, D-complex structures in the sense of F. R. Harvey and H. B. Law…
Proves graph 3-manifold groups have two specific properties.
We study deformations of Lie groupoids by means of the cohomology which controls them. This cohomology turns out to provide an intrinsic model for the cohomology of a Lie groupoid with values in its adjoint representation. We prove several fundamental properties of the deformation cohomology including Morita invariance…
Study on almost complex structures with maximal Nijenhuis tensor rank and cohomological properties.