Stable triples, equivariant bundles and dimensional reduction
نویسندگان
چکیده
منابع مشابه
Equivariant Spectral Triples
We present the review of noncommutative symmetries applied to Connes’ formulation of spectral triples. We introduce the notion of equivariant spectral triples with Hopf algebras as isometries of noncommutative manifolds, relate it to other elements of theory (equivariant K-theory, homology, equivariant differential algebras) and provide several examples of spectral triples with their isometries...
متن کاملEquivariant Bundles and Isotropy Representations
We introduce a new construction, the isotropy groupoid, to organize the orbit data for split Γ-spaces. We show that equivariant principal G-bundles over split Γ-CW complexes X can be effectively classified by means of representations of their isotropy groupoids. For instance, if the quotient complex A = Γ\X is a graph, with all edge stabilizers toral subgroups of Γ, we obtain a purely combinato...
متن کاملEquivariant bundles and adapted connections
Given a complex manifold M equipped with a holomorphic action of a connected complex Lie group G, and a holomorphic principal H–bundle EH over X equipped with a G–connection h, we investigate the connections on the principal H–bundle EH that are (strongly) adapted to h. Examples are provided by holomorphic principal H– bundles equipped with a flat partial connection over a foliated manifold.
متن کاملQuantization of Equivariant Vector Bundles
The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry group.) In preparation for the main result, the quantization of coadjoint orbits is discussed in detail. This subject should not be confused with the quanti...
متن کاملConstruction of Equivariant Vector Bundles
Let X be the wonderful compactification of a complex adjoint symmetric space G/K such that rk(G/K) = rk(G) − rk(K). We show how to extend equivariant vector bundles on G/K to equivariant vector bundles on X , generated by their global sections and having trivial higher cohomology groups. This relies on a geometric construction of equivariant vector bundles in the setting of varieties with reduc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 1996
ISSN: 0025-5831,1432-1807
DOI: 10.1007/bf01446292