Flat bundles with solvable holonomy
نویسندگان
چکیده
منابع مشابه
Primitive Compact Flat Manifolds with Holonomy Group
From an important construction of Calabi (see [Ca], [Wo]), it follows that the compact Riemannian flat manifolds with first Betti number zero are the building blocks for all compact Riemannian flat manifolds. It is, therefore, of interest to construct families of such objects. These are often called primitive manifolds. Hantzsche and Wendt (1935) constructed the only existing 3-dimensional comp...
متن کاملRicci-Flat Holonomy: a Classification
The reductive holonomy algebras for a torsion-free affine connection are analysed, with the goal of establishing which ones can correspond to a Ricci-flat connection with the same properties. Various families of holonomies are eliminated through different algebraic means, and examples are constructed (in this paper and in ‘Projective Geometry II: Holonomy Classification’, by the same author) in...
متن کاملEquivariant Holonomy for Bundles and Abelian Gerbes
This paper generalizes Bismut’s equivariant Chern character to the setting of abelian gerbes. In particular, associated to an abelian gerbe with connection, an equivariantly closed differential form is constructed on the space of maps of a torus into the manifold. These constructions are made explicit using a new local version of the higher Hochschild complex, resulting in differential forms gi...
متن کاملNonnegatively Curved Vector Bundles with Large Normal Holonomy Groups
When B is a biquotient, we show that there exist vector bundles over B with metrics of nonnegative curvature whose normal holonomy groups have arbitrarily large dimension.
متن کاملCharacteristic Classes of Foliated Surface Bundles with Area-preserving Holonomy
Making use of the extended flux homomorphism defined in [13] on the group SympΣg of symplectomorphisms of a closed oriented surface Σg of genus g ≥ 2, we introduce new characteristic classes of foliated surface bundles with symplectic, equivalently area-preserving, total holonomy. These characteristic classes are stable with respect to g and we show that they are highly non-trivial. We also pro...
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: Proceedings of the American Mathematical Society
سال: 1981
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1981-0612747-0