Characteristic Classes of Quantum Principal Bundles
نویسنده
چکیده
A noncommutative-geometric generalization of classical Weil theory of characteristic classes is presented, in the conceptual framework of quantum principal bundles. A particular care is given to the case when the bundle does not admit regular connections. A cohomological description of the domain of the Weil homomorphism is given. Relations between universal characteristic classes for the regular and the general case are analyzed. In analogy with classical geometry, a natural spectral sequence is introduced and investigated. The appropriate counterpart of the Chern character is constructed, for structures admitting regular connections. Illustrative examples and constructions are presented.
منابع مشابه
ar X iv : q - a lg / 9 60 50 08 v 1 5 M ay 1 99 6 QUANTUM PRINCIPAL BUNDLES & THEIR CHARACTERISTIC CLASSES
A general theory of characteristic classes of quantum principal bundles is sketched, incorporating basic ideas of classical Weil theory into the conceptual framework of non-commutative differential geometry. A purely cohomological interpretation of the Weil homomorphism is given, together with a geometrical interpretation via quantum invariant polynomials. A natural spectral sequence is describ...
متن کاملCharacteristic classes in the Chow ring
Let G be a reductive algebraic group over an algebraically closed field k. An algebraic characteristic class of degree i for principal G-bundles on schemes is a function c assigning to each principal G-bundle E → X an element c(E) in the Chow group AX, natural with respect to pullbacks. These classes are analogous to topological characteristic classes (which take values in cohomology), and two ...
متن کاملGroupoid extensions, principal 2-group bundles and characteristic classes
We give an explicit description of a 1-1 correspondence between Morita equivalence classes of, on the one hand, principal 2-group [G → Aut(G)]bundles over Lie groupoids (i.e. [G → Aut(G)]-bundles over differentiable stacks) and, on the other hand, centralG-extensions of Lie groupoids (i.e. Ggerbes over differentiable stacks). We also introduce universal characteristic classes for 2-group bundle...
متن کاملPrincipal Bundles on Projective Varieties and the Donaldson-uhlenbeck Compactification
Let H be a semisimple algebraic group. We prove the semistable reduction theorem for μ–semistable principal H–bundles over a smooth projective variety X defined over the field C. When X is a smooth projective surface and H is simple, we construct the algebro– geometric Donaldson–Uhlenbeck compactification of the moduli space of μ–semistable principal H–bundles with fixed characteristic classes ...
متن کاملBundles, Classifying Spaces and Characteristic Classes
Introduction 1 1. Bundles 2 1.1. Pullback 2 1.2. Sections 3 1.3. Fiber bundles as fibrations 4 2. Vector bundles 4 2.1. Whitney sum 5 2.2. Sections of vector bundles 6 2.3. Inner products 6 3. Principal Bundles 7 3.1. Morphisms 7 3.2. Sections and trivializations 8 3.3. Associated bundles 9 3.4. Homotopy classification 11 3.5. B as a functor 14 4. Characteristic classes 16 4.1. Line Bundles 16 ...
متن کامل