Flag Foliations Functionals. the Hopf Hypothesi
نویسنده
چکیده
With the help of a new type of functionals we study manifolds diffeomorphic to S 2 × S 2 and establish, in particular, the Hopf conjecture.
منابع مشابه
On the k-nullity foliations in Finsler geometry
Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive...
متن کاملLessons from Quantum Field Theory Hopf Algebras and Spacetime Geometries
We discuss the prominence of Hopf algebras in recent progress in Quantum Field Theory. In particular, we will consider the Hopf algebra of renormalization, whose antipode turned out to be the key to a conceptual understanding of the subtraction procedure. We shall then describe several occurences of this, or closely related Hopf algebras, in other mathematical domains, such as foliations, Runge...
متن کاملNonuniformisable Foliations on Compact Complex Surfaces
We give a complete classification of holomorphic foliations on compact complex surfaces which are not uniformisable, i.e., for which universal coverings of the leaves do not glue together in a Hausdorff way. This leads to complex analogs of the Reeb component defined on certain Hopf surfaces and certain Kato surfaces. 2000 Math. Subj. Class. 32J15, 37F75, 57R30.
متن کاملHopf Algebras, Renormalization and Noncommutative Geometry
We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of tranverse index theory for foliations.
متن کاملLinking Numbers of Measured Foliations
We generalise the average asymptotic linking number of a pair of divergence-free vector fields on homology threespheres [1, 2, 14] by considering the linking of a divergence-free vector field on a manifold of arbitrary dimension with a codimension two foliation endowed with an invariant transverse measure. We prove that the average asymptotic linking number is given by an integral of Hopf type....
متن کامل