The Diagonal Cohomology Class of Vertical Bundles
نویسنده
چکیده
Given a manifold M , Milnor and Stasheff studied in [1] the diagonal cohomology class u′′ ∈ Hm(M ×M ;Z/2) that describes the orientation of the tangent bundle, and is related to its Stiefel-Whitney Classes. We generalize this concept to fiber bundles M → E → N where the fiber and base are manifolds, relate it to the diagonal homology class, study the naturality of the construction, give further characterizations of the class, and compute it for certain examples.
منابع مشابه
Para-Kahler tangent bundles of constant para-holomorphic sectional curvature
We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagona...
متن کاملSupernatural Analogues of Beilinson Monads
We use supernatural bundles to build GL-equivariant resolutions supported on the diagonal of Pn × Pn, in a way that extends Beilinson’s resolution of the diagonal. We thus obtain results about supernatural bundles that largely parallel known results about exceptional collections. We apply this construction to Boij–Söderberg decompositions of cohomology tables of vector bundles, yielding a proof...
متن کاملChern Invariants of Some Flat Bundles in the Arithmetic Deligne Cohomology
In this note, we investigate the cycle class map between the rational Chow groups and the arithmetic Deligne cohomology, introduced by Green-Griffiths and AsakuraSaito. We show nontriviality of the Chern classes of flat bundles in the arithmetic Deligne Cohomology in some cases and our proofs also indicate that generic flat bundles can be expected to have nontrivial classes. This provides examp...
متن کاملMathai-quillen Formalism
Characteristic classes play an essential role in the study of global properties of vector bundles. Particularly important is the Euler class of real orientable vector bundles. A de Rham representative of the Euler class (for tangent bundles) first appeared in Chern’s generalisation of the Gauss-Bonnet theorem to higher dimensions. The representative is the Pfaffian of the curvature, whose cohom...
متن کاملOn the property of for a second-order system with zero diagonal coefficient
Abstract: This paper investigates the problem of whether all trajectories of the system and cross the vertical isocline, which is very important for the existence of periodic solutions and oscillation theory. Sufficient conditions are given for all trajectories to cross the vertical isocline.
متن کامل