相关论文: Characteristic classes of Higgs bundles and Reznik…
For a semisimple real Lie group $G$, we study topological properties of moduli spaces of polystable parabolic $G$-Higgs bundles over a Riemann surface with a divisor of finitely many distinct points. For a split real form of a complex…
On a compact $\partial\bar\partial$-manifold $X$, one has the Hodge decomposition: the de Rham cohomology groups split into subspaces of pure-type classes as $H_{dR}^k (X)=\oplus_{p+q=k}H^{p,\,q}(X)$, where the $H^{p,\,q}(X)$ are…
We introduce a notion of ellipticity of complexes of linear pseudodifferential operators acting on sections of $A$-Hilbert bundles over smooth manifolds, $A$ being a $C^*$-algebra. We prove that the cohomology groups of an $A$-elliptic…
We prove the existence of many non-trivial characteristic classes of smooth oriented bundles with fibre a product $ S^{n}\times S^{n} $ of odd-dimensional spheres. We do so by proving injectivity of the map from the ring of rational…
We show that every orbispace satisfying certain mild hypotheses has 'enough' vector bundles. It follows that the K-theory of finite rank vector bundles on such orbispaces is a cohomology theory. Global presentation results for smooth…
In this paper, we construct new characteristic classes of fiber bundles via flat connections with values in infinite-dimensional Lie algberas of derivations. In fact, choosing a fiberwise metric, we construct a chain map to the de Rham…
In this paper we give a gauge theoretic construction of the joint moduli space of stable G-Higgs bundles on closed Riemann surfaces, where the Riemann surface structure is allowed to vary in the Teichm\"uller space of the underlying smooth…
The moduli space of stable bundles of rank 2 and degree 1 on a Riemann surface has rational cohomology generated by the so-called universal classes. The work of Baranovsky, King-Newstead, Siebert-Tian and Zagier provided a complete set of…
Exploiting the description of rings of differential operators as Azumaya algebras on cotangent bundles, we show that the moduli stack of flat connections on a curve (allowed to acquire orbifold points) defined over an algebraically closed…
We introduce several families of filtrations on the space of vector bundles over a smooth projective variety. These filtrations are defined using the large k asymptotics of the kernel of the Dolbeault Dirac operator on a bundle twisted by…
We establish the correspondence between tame harmonic bundles and $\mu_L$-stable parabolic Higgs bundles with trivial characteristic numbers. We also show the Bogomolov-Gieseker type inequality for $\mu_L$-stable parabolic Higgs bundles.…
In this paper, we prove a nonabelian Hodge correspondence for principal bundles on a smooth variety $X$ in positive characteristic, which generalizes the Ogus-Vologodsky correspondence for vector bundles. Then we extend the correspondence…
This monograph is devoted to the theory of vector-valued modular forms for orthogonal groups of signature (2,n). Our purpose is multi-layered: (1) to lay a foundation of the theory of vector-valued orthogonal modular forms; (2) to develop…
We describe new families of the Knizhnik-Zamolodchikov-Bernard (KZB) equations related to the WZW-theory corresponding to the adjoint $G$-bundles of different topological types over complex curves $\Sigma_{g,n}$ of genus $g$ with $n$ marked…
After providing a suitable definition of numerical effectiveness for Higgs bundles, and a related notion of numerical flatness, in this paper we prove, together with some side results, that all Chern classes of a Higgs-numerically flat…
Let G be a reductive group over an algebraically closed field of positive characteristic. Let C be a smooth projective curve over k. We give a description of the moduli space of flat G-bundles in terms of the moduli space of G-Higgs bundles…
We develop a framework to compute characteristic classes and their forms in the computer algebra system SageMath using symbolic calculus. In order to do this, we make use of the Chern-Weil approach in which characteristic classes of vector…
We give a construction of cyclic cocycles representing the equivariant characteristic classes of equivariant bundles. Our formulas generalize Connes' Godbillon-Vey cyclic cocycle. An essential tool of our construction is Connes-Moscovici's…
We look more closely at the higher nonabelian de Rham cohomology of a smooth projective variety or family of varieties that had been defined in some previous papers. We formalize using $n$-stacks the notion of shape underlying this…
M. Kontsevich constructed universal characteristic classes of smooth bundles with fiber a framed odd-dimensional integral homology sphere. In dimension 3, they are known to give a universal finite type invariants of homology 3-spheres.…