相关论文: Differential characters as stacks and prequantizat…
We describe equivariant differential characters (classifying equivariant circle bundles with connections), their prequantization, and reduction.
We show how characteristic classes determine equivariant prequantization bundles over the space of connections on a principal bundle. These bundles are shown to generalize the Chern-Simons line bundles to arbitrary dimensions. Our result…
On a complex symplectic manifold, we construct the stack of quantization-deformation modules, that is, (twisted) modules of microdifferential operators with an extra central parameter, a substitute to the lack of homogeneity. We also…
We introduce a new homological machine for the study of secondary geometric invariants. The objects, called spark complexes, occur in many areas of mathematics. The theory is applied here to establish the equivalence of a large family of…
Using a nonlinear version of the tautological bundle over Gra{\ss}mannians, we construct a transgression map for differential characters from $M$ to the nonlinear Gra{\ss}mannians $\mathrm{Gr}^S(M)$ of submanifolds of $M$ of a fixed type…
A review of the characterization of principal bundles, through the different properties of the action of a group and its related canonical and translation maps, is presented. The work is divided in three stages: a topological group acting…
Let $\pi\colon P\to M$ be a principal bundle and $p$ an invariant polynomial of degree r on the Lie algebra of the structure group. The theory of Chern-Simons differential characters is exploited to define an homology map $\chi^{k} :…
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…
The geometric quantization of a symplectic manifold endowed with a prequantum bundle and a metaplectic structure is defined by means of an integrable complex structure. We prove that its semi-classical limit does not depend on the choice of…
We present examples of prequantizations over integral symplectic manifolds which admit infinitely many smoothly trivial contact mapping classes. These classes are given by the connected components of the strict contactomorphism group which…
A prequantization bundle is a negative circle bundle over a symplectic surface together with a contact form induced by a S1-invariant connection. Given a symplectically aspherical symplectic filling of a prequantization bundle satisfying…
We construct the odd symplectic structure and the equivariant even (pre)symplectic one from it on the space of differential forms on the Riemann manifold. The Poincare -- Cartan like invariants of the second structure define the equivariant…
A tangent category is a categorical abstraction of the tangent bundle construction for smooth manifolds. In that context, Cockett and Cruttwell develop the notion of differential bundle which, by work of MacAdam, generalizes the notion of…
We give a construction of algebraic differential characters, receiving classes of algebraic bundles with connection, lifitng the Chern-Simons invariants defined with S. Bloch, the classes in the Chow group and the analytic secondary…
We adapt the framework of geometric quantization to the polysymplectic setting. Considering prequantization as the extension of symmetries from an underlying polysymplectic manifold to the space of sections of a Hermitian vector bundle, a…
We construct connections and characteristic forms for principal bundles over groupoids and stacks in the differentiable, holomorphic and algebraic category using Atiyah sequences associated to transversal tangential distributions.
We promote geometric prequantization to higher geometry (higher stacks), where a prequantization is given by a higher principal connection (a higher gerbe with connection). We show fairly generally how there is canonically a tower of higher…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
We compute the connective differential $K$-theory and the differential cohomology of the moduli stack of principal $G$-bundles with connection. The results are formulated in terms of invariant polynomials and the representation ring of $G$.…
In the first part of this paper, we propose a uniform interpretation of characteristic classes as obstructions to the reduction of the structure group and to the existence of an equivariant extension of a certain homomorphism defined a…