Homogeneous C R-manifolds.
Homological Transfers for Orbit Space Projections.
Homotopy nilpotent Lie groups have no torsion in homology.
Hopf Structures on Stiefel Manifolds.
Le complexe de Koszul en algèbre et topologie
The Koszul complex, as introduced in 1950, was a differential graded algebra which modelled a principal fibre bundle. Since then it has been an effective tool, both in algebra and in topology, for the calculation of homological and homotopical invariants. After a partial summary of these results we recall more recent generalizations of this complex, and some applications.
Line Bundles over Framed Manifolds.
Locally finite approximation of Lie groups, I.
Nilpotent complex structures.
Este artículo presenta un panorama de algunos resultados recientes sobre estructuras complejas nilpotentes J definidas sobre nilvariedades compactas. Tratamos el problema de clasificación de nilvariedades compactas que admiten una tal J, el estudio de un modelo minimal de Dolbeault y su formalidad, y la construcción de estructuras complejas nilpotentes para las cuales la sucesión espectral de Frölicher no colapsa en el segundo término.
Non-vanishing on the first cohomology
Nonzero degree tangential maps between dual symmetric spaces.
On Lusternik-Schnirelmann category of SO(10)
Let G be a compact connected Lie group and p: E → ΣA be a principal G-bundle with a characteristic map α: A → G, where A = ΣA₀ for some A₀. Let with F₀ = ∗, F₁ = ΣK₁ and Fₘ ≃ G be a cone-decomposition of G of length m and F’₁ = ΣK’₁ ⊂ F₁ with K’₁ ⊂ K₁ which satisfy up to homotopy for all i. Then cat(E) ≤ m + 1, under suitable conditions, which is used to determine cat(SO(10)). A similar result was obtained by Kono and the first author (2007) to determine cat(Spin(9)), but that result could not...
On parabolic Whittaker functions II
We propose a Givental-type stationary phase integral representation for the restricted Grm,N-Whittaker function, which is expected to describe the (S 1×U N)-equivariant Gromov-Witten invariants of the Grassmann variety Grm,N. Our key tool is a generalization of the Whittaker model for principal series U(gl N)-modules, and its realization in the space of functions of totally positive unipotent matrices. In particular, our construction involves a representation theoretic derivation of the Batyrev-Ciocan-Fontanine-Kim-van...
On p-equivalences and p-universal spaces
On the differential form spectrum of hyperbolic manifolds
We give a lower bound for the bottom of the differential form spectrum on hyperbolic manifolds, generalizing thus a well-known result due to Sullivan and Corlette in the function case. Our method is based on the study of the resolvent associated with the Hodge-de Rham laplacian and leads to applications for the (co)homology and topology of certain classes of hyperbolic manifolds.
On the Stiefel-Whitney classes and the span of real Grassmannians
On the topology of double coset manifolds.
On two results of Singhof
For a compact connected semisimple Lie group we shall prove two results (both related with Singhof’s paper [13]) on the Lusternik-Schnirelmann category of the adjoint orbits of , respectively the 1-dimensional relative category of a maximal torus in . The techniques will be classical, but we shall also apply some basic results concerning the so-called -category (cf. [14]).
Parallelizability of Homogeneous Spaces. I.
Pontryagin forms on homogeneous spaces.
Propriétés de Lefschetz dans la cohomologie de certaines variétés arithmétiques : le cas des surfaces modulaires de Hilbert