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91.
Max Karoubi 《K-Theory》1990,4(1):55-87
Résumé Dans cet article nous définissons un nouveau foncteur MK(X), K-théorie multiplicative de X, dans lequel prennent leurs valeurs les classes caractéristiques primaires et secondaires connues de fibrés vectoriels munis de structures supplementaires. Il s'agit notamment des classes caractéristiques de fibrés plats, feuilletés ou holomorphes ainsi que des régulateurs en K-théorie algébrique.
In this paper we define a new functor MK(X), multiplicative K-theory of X, which is the target of known characteristic classes (primary and secondary) of vector bundles provided with additional structures. One should mention characteristic classes of flat, foliated or holomorphic vector bundles as well as regulators in algebraic K-theory.
A Alexander Grothendieck pour son 60e anniversaire 相似文献
92.
Let G be a connected noncompact semisimple Lie group with finite center, K a maximal compact subgroup, and X a compact manifold (or more generally, a Borel space) on which G acts. Assume that ν is a μ -stationary measure on X, where μ is an admissible measure on G, and that the G-action is essentially free. We consider the foliation of K\ X with Riemmanian leaves isometric to the symmetric space K\ G, and the associated tangential bounded de-Rham cohomology, which we show is an invariant of the action. We prove both vanishing
and nonvanishing results for bounded tangential cohomology, whose range is dictated by the size of the maximal projective
factor G/Q of (X, ν). We give examples showing that the results are often best possible. For the proofs we formulate a bounded tangential version
of Stokes’ theorem, and establish a bounded tangential version of Poincaré’s Lemma. These results are made possible by the
structure theory of semisimple Lie groups actions with stationary measure developed in Nevo and Zimmer [Ann of Math. 156, 565--594]. The structure theory assert, in particular, that the G-action is orbit equivalent to an action of a uniquely determined parabolic subgroup Q. The existence of Q allows us to establish Stokes’ and Poincaré’s Lemmas, and we show that it is the size of Q (determined by the entropy) which controls the bounded tangential cohomology.
Supported by BSF and ISF.
Supported by BSF and NSF. 相似文献
93.
Bounds on leaves of one-dimensional foliations 总被引:1,自引:0,他引:1
Let X be a variety over
an algebraically closed field,
a onedimensional
singular foliation, and
a projective leaf of .
We prove that
where p
a
(C) is the arithmetic genus, where
(C) is the colength in the
dualizing sheaf of the subsheaf generated by the Kähler
differentials, and where S is
the singular locus of . We bound (C) and
, and then improve and
extend some recent results of Campillo, Carnicer, and de la
Fuente, and of du Plessis and Wall.Dedicated to IMPA on the occasion of its 50th anniversary 相似文献
94.
Gianluca Bande 《Transactions of the American Mathematical Society》2003,355(4):1699-1711
We introduce a new geometric structure on differentiable manifolds. A contact-symplectic pair on a manifold is a pair where is a Pfaffian form of constant class and a -form of constant class such that is a volume form. Each form has a characteristic foliation whose leaves are symplectic and contact manifolds respectively. These foliations are transverse and complementary. Some other differential objects are associated to it. We give a local model and several existence theorems on nilpotent Lie groups, nilmanifolds and principal torus bundles. As a deep application of this theory, we give a negative answer to the famous Reeb's problem which asks if every vector field without closed 1-codimensional transversal on a manifold having contact forms is the Reeb vector field of a contact form.
95.
Let be a holomorphic foliation with ample canonical bundle on a smooth projective surface X. We obtain an upper bound on the order of its automorphism group which depends only on and provided this group is finite. Here, and are the canonical bundles of and X, respectively. 相似文献
96.
In this note we discuss a few properties of transnormal Finsler functions, i.e., the natural generalization of distance functions and isoparametric Finsler functions. In particular, we prove that critical level sets of an analytic transnormal function are submanifolds, and the partition of M into level sets is a Finsler partition, when the function is defined on a compact analytic manifold M. 相似文献
97.
Ruben Lizarbe 《Mathematische Nachrichten》2023,296(9):3877-3891
We prove that a generic holomorphic foliation on a weighted projective plane has no algebraic solutions when the degree is big enough. We also prove an analogous result for foliations on Hirzebruch surfaces. 相似文献
98.
We study the conormal sheaves and singular schemes of one-dimensional foliations on smooth projective varieties X of dimension 3 and Picard rank 1. We prove that if the singular scheme has dimension 0, then the conormal sheaf is μ-stable whenever the tangent bundle is stable, and apply this fact to the characterization of certain irreducible components of the moduli space of rank 2 reflexive sheaves on and on a smooth quadric hypersurface . Finally, we give a classification of local complete intersection foliations, that is, foliations with locally free conormal sheaves, of degree 0 and 1 on Q3. 相似文献