arXiv research

Cohomology of 'book' Lie algebra Poisson structure computed.

Algorithm calculates stable multiplicities in cohomology of configuration spaces.

The blow-down map is studied in Lie algebroid cohomology.

Compute symplectic cohomology of cAn singularities.

We consider semi-direct products $\C^{n}\ltimes_φN$ of Lie groups with lattices $Γ$ such that $N$ are nilpotent Lie groups with left-invariant complex structures. We compute the Dolbeault cohomology of direct sums of holomorphic line bundles over $G/Γ$ by using the Dolbeaut cohomology of the Lie algebras of the direct …

Compute local cohomology of vector fields on manifolds.

Researchers compute the cohomology of an elliptic tangent bundle.

New computations show various properties of bounded cohomology in finitely presented groups.

Researchers compute Dolbeault cohomology of Endo-Pajitnov manifolds.

The rational cohomology ring of A_3, the moduli space of abelian 3-folds is computed. This is isomorphic to the the rational cohomology ring of the group Sp_3(Z) of 6x6 integral symplectic matrices. The main ingredients in the computation are (1) Looijenga's computation of the rational cohomology ring of M_3, the modul…

Homology and cohomology theory for topological quandles computed.

Classifies and computes cohomologies of complex structures on Lie groups.

Let $G$ be a simply connected solvable Lie group with a lattice $Γ$ and $N$ the nilradical of $G$. For a complex valued representation $ρ: G\to GL(V_ρ)$ such that the restriction $ρ_{|_{N}}$ is unipotent, as an advanced variation of cohomology computation of solvmanifolds by using Lie algebra cohomology, we construct a…

Study symplectic cohomology of certain singularities using homological mirror symmetry.

Paper computes rational cohomology of spin hyperelliptic mapping class groups.

Researchers compute the cohomology ring of a foliation defined by a group action.

Motivated by orbifold string theory, we introduce orbifold cohomology group for any almost complex orbifold and orbifold Dolbeault cohomology for any complex orbifold. Then, we show that our new cohomology group satisfies Poincare duality and has a natural ring structure. Some examples of orbifold cohomology ring are c…

In this note several computations of equivariant cohomology groups are performed. For the compactly supported equivariant cohomology, the notion of infinitesimal index developed in arXiv:1003.3525, allows to describe these groups in terms of certain spaces of distributions arising in the theory of splines. The new vers…

We try to generalize the Poisson cohomology of a 2-dimensional Poisson manifold to the n-vectors on a n-dimensional manifold. We define several cohomologies and we compute locally some of them, in the case of germs at 0 of n-vectors on a real or complex vector field of dimension n.

We solve some computational problems for triangulated closed three-dimensional manifolds using groups of simplicial homology and cohomology modulo 2. Two efficient algorithms for computing the intersection numbers of 1- and 2-dimensional cycles are developed. By means of these algorithms it is possible to construct a b…

In this paper we describe methods for computing rack and quandle cohomology. We illustrate these methods by completely determining the cohomology of prime dihedral quandles.

Researchers compute cohomology of mapping class groups with Prym representations, showing instability for large genus.

Study computes SL(2,C) Floer cohomology for surgeries on knots.

We present some general results on properties of the bihamiltonian cohomologies associated to bihamiltonian structures of hydrodynamic type, and compute the third cohomology for the bihamiltonian structure of the dispersionless KdV hierarchy. The result of the computation enables us to prove the existence of bihamilton…

We propose a method for calculating cohomology operations for finite simplicial complexes. Of course, there exist well--known methods for computing (co)homology groups, for example, the reduction algorithm consisting in reducing the matrices corresponding to the differential in each dimension to the Smith normal form, …

We study conditions under which sub-complexes of a double complex of vector spaces allow to compute the Bott-Chern cohomology. We are especially aimed at studying the Bott-Chern cohomology of special classes of solvmanifolds, namely, complex parallelizable solvmanifolds and solvmanifolds of splitting type. More precise…

We show that the group cohomology of torsion-free virtually polycyclic groups and the continuous cohomology of simply connected solvable Lie groups can be computed by the rational cohomology of algebraic groups. Our results are generalizations of certian results on the cohomology of solvmanifolds and infra-solvmanifold…

New complexes derived from any filtered cochain complex compute the same cohomology.

In this paper we study Morse homology and cohomology with local coefficients, i.e. "twisted" Morse homology and cohomology, on closed finite dimensional smooth manifolds. We prove a Morse theoretic version of Eilenberg's Theorem, and we prove isomorphisms between twisted Morse homology, Steenrod's CW-homology with loca…

The paper studies deformations of symplectic groupoids using cohomology and spectral sequences.

We compute the compactly supported cohomology of the standard realization of any locally finite building.

The article examines twisted cohomologies on algebraic and analytic varieties.

Compute Dolbeault and Bott-Chern cohomologies of complex solvmanifolds.

We discuss the known evidence for the conjecture that the Dolbeault cohomology of nilmanifolds with left-invariant complex structure can be computed as Lie-algebra cohomology and also mention some applications.

In this note, we compute the Poisson cohomology groups for any Poisson Del Pezzo surface.

Compute group cohomology for mapping class group with non-symplectic coefficients.

Paper shows hyperbolic 3-manifolds can sound the same but have different cohomology.

We introduce a bicomplex which computes the triple cohomology of Lie--Rinehart algebras. We prove that the triple cohomology is isomorphic to the Rinehart cohomology \cite{Ri} provided the Lie--Rinehart algebra is projective over the corresponding commutative algebra. As an application we construct a canonical class in…

Using spectral sequences techniques we compute the bihamiltonian cohomology groups of the pencil of Poisson brackets of dispersionless KdV hierarchy. In particular this proves a conjecture of Liu and Zhang about the vanishing of such cohomology groups.

We study Bott-Chern cohomology on compact complex non-Kähler surfaces. In particular, we compute such a cohomology for compact complex surfaces in class $\text{VII}$ and for compact complex surfaces diffeomorphic to solvmanifolds.

We prove that, for some classes of complex nilmanifolds, the Bott-Chern cohomology is completely determined by the Lie algebra associated to the nilmanifold with the induced complex structure. We use these tools to compute the Bott-Chern and Aeppli cohomologies of the Iwasawa manifold and of its small deformations, com…

It is known that the computation of the Poisson cohomology is closely related to the classification of singularities of Poisson structures. In this paper, we will first look for the normal forms of germs at (0,0) of Poisson structures on the real (or complex) plane and recall a result given by Arnold. Then, we will com…

New techniques compute $L^2$-cohomology of quasi-fibered metrics.

In this paper we study the cohomology of (strict) Lie 2-groups. We obtain an explicit Bott-Shulman type map in the case of a Lie 2-group corresponding to the crossed module $A\to 1$. The cohomology of the Lie 2-groups corresponding to the universal crossed modules $G\to \Aut(G)$ and $G\to \Aut^+(G)$ is the abutment of …

Relations between parameter rigidity of locally free Lie group actions on closed manifolds and the 1st leafwise cohomology of the orbit foliations are discussed. Some computational results of the leafwise cohomology are included.

This paper computes fixed point Floer cohomology for Dehn twists on surfaces.

Deep analysis of KV-Poisson structures and new invariant computed.

A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second cohomology groups for specific topological quandles. A method of computing the c…