Tangential Cobordism.
Tangential homotopy equivalences.
Taut foliations of 3-manifolds and suspensions of
Let be a compact oriented 3-manifold whose boundary contains a single torus and let be a taut foliation on whose restriction to has a Reeb component. The main technical result of the paper, asserts that if is obtained by Dehn filling along any curve not parallel to the Reeb component, then has a taut foliation.
Tenseness of Riemannian flows
We show that any transversally complete Riemannian foliation of dimension one on any possibly non-compact manifold is tense; namely, admits a Riemannian metric such that the mean curvature form of is basic. This is a partial generalization of a result of Domínguez, which says that any Riemannian foliation on any compact manifold is tense. Our proof is based on some results of Molino and Sergiescu, and it is simpler than the original proof by Domínguez. As an application, we generalize some...
TFT Construction of RCFT correlators. V: Proof of modular invariance and factorisation.
The ℤ₂-cohomology cup-length of real flag manifolds
Using fiberings, we determine the cup-length and the Lyusternik-Shnirel’man category for some infinite families of real flag manifolds , q ≥ 3. We also give, or describe ways to obtain, interesting estimates for the cup-length of any , q ≥ 3. To present another approach (combining well with the “method of fiberings”), we generalize to the real flag manifolds Stong’s approach used for calculations in the ℤ₂-cohomology algebra of the Grassmann manifolds.
The algebraic theory of finiteness obstruction.
The analytic Carathéodory conjecture.
The angle defect for arbitrary polyhedra.
The asymptotic behavior of invariant collective motion.
The BIC of a singular foliation defined by an abelian group of isometries
We study the cohomology properties of the singular foliation ℱ determined by an action Φ: G × M → M where the abelian Lie group G preserves a riemannian metric on the compact manifold M. More precisely, we prove that the basic intersection cohomology is finite-dimensional and satisfies the Poincaré duality. This duality includes two well known situations: ∙ Poincaré duality for basic cohomology (the action Φ is almost free). ∙ Poincaré duality for intersection cohomology (the group G is compact...
The Bloch invariant as a characteristic class in .
The C*-algebras of codimension one foliations without holonomy.
The Canonical Class and the Properties of Kähler Surfaces.
The characterization of strictly parabolic manifolds
The Chern Classes of the Stable Rank 3 Vector Bundles on IP3.
The Chern numbers of holomorphic vector bundles and formally holomorphic connections of complex vector bundles over almost complex manifolds.
The chess conjecture.
The classification of weighted projective spaces
We obtain two classifications of weighted projective spaces: up to hoeomorphism and up to homotopy equivalence. We show that the former coincides with Al Amrani's classification up to isomorphism of algebraic varieties, and deduce the latter by proving that the Mislin genus of any weighted projective space is rigid.
The cobordism of Real manifolds
We calculate completely the Real cobordism groups, introduced by Landweber and Fujii, in terms of homotopy groups of known spectra.