Related papers: Characteristic Classes on Grassmann Manifolds

C*-endomorphisms arising from superselection structures with non-trivial centre define a 'rank' and a 'first Chern class'. Crossed products by such endomorphisms involve the Cuntz-Pimsner algebra of a vector bundle having the…

We show by studying the symplectic geometry of the extended moduli space that the intersection cohomology of the representation space $Hom(\pi_1(\Sigma),G)/G$ for a simply connected compact Lie group $G$ is naturally embedded into the $G$…

Let GO(2n) be the general orthogonal group (the group of similitudes) over any algebraically closed field of characteristic not equal to 2. We determine the etale cohomology ring with mod 2 coefficients of the algebraic stack BGO(2n). In…

Let $M_{n,k}$ denote the even orthogonal Grassmanian, $SO(2n) / (U(k) \times SO(2n-2k) )$. We study endomorphisms of the rational cohomology algebra of $M_{n,k}$. We prove that an endomorphism of the rational cohomology algebra of…

Let $K/E/\mathbb{Q}_p$ be a tower of finite extensions with $E$ Galois. We relate the category of $G_K$-equivariant vector bundles on the Fargues--Fontaine curve with coefficients in $E$ with $E$-$G_K$-$B$-pairs and describe crystalline and…

Let $X$ be a compact K\"ahler manifold. The set $\cha(X)$ of one-dimensional complex valued characters of the fundamental group of $X$ forms an algebraic group. Consider the subset of $\cha(X)$ consisting of those characters for which the…

We prove a duality for factorization homology which generalizes both usual Poincar\'e duality for manifolds and Koszul duality for $\mathcal{E}_n$-algebras. The duality has application to the Hochschild homology of associative algebras and…

The Poincare duality of classical cohomology and the extension of this duality to quantum cohomology endows these rings with the structure of a Frobenius algebra. Any such algebra possesses a canonical ``characteristic element;'' in the…

For $4 \nmid L$ and $g$ large, we calculate the integral Picard groups of the moduli spaces of curves and principally polarized abelian varieties with level $L$ structures. In particular, we determine the divisibility properties of the…

Let G be a topological group such that its homology H(G) with coefficients in a principal ideal domain R is an exterior algebra, generated in odd degrees. We show that the singular cochain functor carries the duality between G-spaces and…

In this paper we survey geometric and arithmetic techniques to study the cohomology of semiprojective hyperkaehler manifolds including toric hyperkaehler varieties, Nakajima quiver varieties and moduli spaces of Higgs bundles on Riemann…

Let $E$ be a holomorphic vector bundle over a compact K\"{a}hler manifold $(X,\omega)$ with negative sectional curvature $sec\leq -K<0$, $\Delta_{E}$ be the Chern connection on $E$. In this article we show that if…

The leitmotiv of this review is noncommutative principal U(1)-bundles and associated line bundles. In the first part I give a brief introduction to Hopf-Galois theory and its applications, from field extensions to principal group actions. I…

In this paper we study the variability and rigidity of secondary characteristic classes which arise from flat connections on a manifold. Considering the connection as a Lie-algebra valued one-form, we study the characteristic map from Lie…

A special linear Grassmann variety SGr(k,n) is the complement to the zero section of the determinant of the tautological vector bundle over Gr(k,n). For a representable ring cohomology theory A(-) with a special linear orientation and…

After introducing the simplicial manifolds, such as the different ways of defining the differential forms on them, we summarized a canonical way of calculating the characteristic classes of a $G$-principal bundle by computing them on the…

We construct and analyse models of equivariant cohomology for differentiable stacks with Lie group actions extending classical results for smooth manifolds due to Borel, Cartan and Getzler. We also derive various spectral sequences for the…

In this paper we show that every rational cohomology class of type $(p,p)$ on a compact K\"ahler manifold can be representated as a differential $(p,p)$-form given by an explicit formula involving a \v{C}ech cocycle. First we represent…

We classify SO(n)-equivariant principal bundles over $S^n$ in terms of their isotropy representations over the north and south poles. This is an example of a general result classifying equivariant $(\Pi, G)$-bundles over cohomogeneity one…

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…