Related papers: Polylogarithms for $GL_2$ over totally real fields

In [5], the notion of polynomial cocycles is used to give an expression for the second cohomology of T-groups with coefficients in a torsion-free nilpotent module. We make this expression concrete in the case of a T-group G of nilpotency…

In this paper, we determine the motive of the classifying torsor of an algebraic torus. As a result, we give an exact sequence describing the degree 4 cohomological invariants of algebraic tori. Using results by Blinstein and Merkurjev,…

We prove a cyclic cohomological analogue of Haefliger's van Est-type theorem for the groupoid of germs of diffeomorphisms of a manifold. The differentiable version of cyclic cohomology is associated to the algebra of transverse differential…

We dualise the classical fact that an operad with multiplication leads to cohomology groups which form a Gerstenhaber algebra to the context of cooperads: as a result, a cooperad with comultiplication induces a homology theory that is…

A diagram of algebras is a functor valued in a category of associative algebras. I construct an operad acting on the Hochschild bicomplex of a diagram of algebras. Using this operad, I give a direct proof that the Hochschild cohomology of a…

Consider a subgroup of finite index of modular group. We give an analytic criterion for a cuspidal divisor to be torsion in the Jacobian of the corresponding modular curve. By BelyI theorem, such a criterion would apply to any curve over a…

The purpose of this article is to newly define the $p$-adic polylogarithm as an equivariant class in the cohomology of a certain infinite disjoint union of algebraic tori associated to a totally real field. We will then express the special…

The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these spaces. In this article, we compute the cohomology groups of line bundles over various holomorphic, non-commutative…

In this paper we prove that on a smooth algebraic variety the HKR-morphism twisted by the square root of the Todd genus gives an isomorphism between the sheaf of poly-vector fields and the sheaf of poly-differential operators, both…

We study the Hochschild cohomology and the Gerstenhaber algebra structure on the algebraic non-commutative torus/quantum torus orbifolds resulting by the action of finite subgroups of $SL_2(\mathbb Z)$. We also examine the Poisson…

We study Tate-Hochschild homology and cohomology for a two-sided Noetherian Gorenstein algebra. These (co)homology groups are defined for all degrees, non-negative as well as negative, and they agree with the usual Hochschild (co)homology…

Given a smooth compact Riemannian manifold $M$ and a Hamiltonian $H$ on the cotangent space $T^*M$, strictly convex and superlinear in the momentum variables, we prove uniqueness of certain ergodic invariant Lagrangian graphs within a given…

We determine the Gerstenhaber structure on the Hochschild cohomology ring of a class of self-injective special biserial algebras. Each of these algebras is presented as a quotient of the path algebra of a certain quiver. In degree one, we…

We survey recent results about the Torelli question for holomorphic-symplectic varieties. Following are the main topics. A Hodge theoretic Torelli theorem. A study of the subgroup W, of the isometry group of the weight 2 Hodge structure,…

The equivariant and ordinary cohomology rings of Hilbert schemes of points on the minimal resolution C^2//G for cyclic G are studied using vertex operator technique, and connections between these rings and the class algebras of wreath…

We construct a cycle in higher Hochschild homology associated to the 2-dimensional torus which represents 2-holonomy of a non-abelian gerbe in the same way the ordinary holonomy of a principal G-bundle gives rise to a cycle in ordinary…

In this paper, we construct a canonical grading on bordered Heegaard Floer homology by homotopy classes of nonvanishing vector fields. This grading is a generalization of our construction of an absolute grading on Heegaard Floer homology…

We study commutative algebras with Gorenstein duality, i.e. algebras $A$ equipped with a non-degenerate bilinear pairing such that $\langle ac,b\rangle=\langle a,bc\rangle$ for any $a,b,c\in A$. If an algebra $A$ is Artinian, such pairing…

Structural pattern recognition describes and classifies data based on the relationships of features and parts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension. Cohomology can provide…

We use the twisted topological trace formula developed in an earlier paper to understand liftings from symplectic to general linear groups. We analyse the lift from $\SP_{2g}$ to $\PGL_{2g+1}$ over the ground field $\Q$ in further detail,…