Rational Pontryagin classes of Euclidean fiber bundles
نویسندگان
چکیده
The rational Pontryagin classes, evaluated on fiber bundles where the is a 2n-dimensional euclidean space, can be nonzero in cohomology dimensions much greater than 4n. This makes striking contrast with classes of vector bundles.
منابع مشابه
Chern Classes of Bundles on Rational Surfaces
Consider the blow up π : X̃ → X of a rational surface X at a point. Let Ṽ be a holomorphic bundle over X̃ whose restriction to the exceptional divisor isO(j)⊕O(−j) and define V = (π∗Ṽ ) . Friedman and Morgan gave the following bounds for the second Chern classes j ≤ c2(Ṽ )− c2(V ) ≤ j 2. We show that these bounds are sharp.
متن کاملLine Bundles, Rational Points and Ideal Classes
In this note, we will use the term “arithmetic variety” for a normal scheme X for which the structure morphism f : X → Spec(Z) is proper and flat. Let V be a proper, normal (not necessarily geometrically connected) variety over Q. Let us choose a normal model for V over Z, that is an arithmetic variety X whose generic fiber is identified with V . Suppose that F is a number field and consider th...
متن کاملFiber bundles and Lie algebras of top spaces
In this paper, by using of Frobenius theorem a relation between Lie subalgebras of the Lie algebra of a top space T and Lie subgroups of T(as a Lie group) is determined. As a result we can consider these spaces by their Lie algebras. We show that a top space with the finite number of identity elements is a C^{∞} principal fiber bundle, by this method we can characterize top spaces.
متن کاملCharacteristic classes of complexified bundles
We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from real vector bundles are computed. We use characteristic classes with the axioms of Milnor and Stasheff [6]. Introduction Definition (Real generator bundles). We consider a real vector bundle F → B and a complex vector bundle E → B over the same base space B. If...
متن کاملCharacteristic Classes of A{bundles
We consider locally trivial bundles over smooth manifolds, whose fibers are finitely generated projective modules over a convenient algebra A. For such a bundle E → X and a bounded reduced cyclic cocycle c on A we construct a sequence chc (E) of de–Rham cohomology classes on X, which are an analog of the classical Chern character. We show that these classes depend only on the cohomology class o...
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: Geometry & Topology
سال: 2021
ISSN: ['1364-0380', '1465-3060']
DOI: https://doi.org/10.2140/gt.2021.25.3351