Jean-Claude Hausmann

Caractéristiques d'euler et groupes fondamentaux des variétés de dimension 4.

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The Space of Clouds in Euclidean Space

We study the space Nd m of clouds in R d (ordered sets of m points modulo the action of the group of affine isometries). We show that Nd m is a smooth space, stratified over a certain hyperplane arrangement in R m . We give an algorithm to list all the chambers and other strata (this is independent of d). With the help of a computer, we obtain the list of all the chambers for m ≤ 9 and all the strata when m ≤ 8. As the strata are the product of a polygon space with a disk, this gives a classification of m-gon spaces for m ≤ 9. When d = 2,3, m = 5, 6, 7, and modulo reordering, we show that the chambers (and so the different generic polygon spaces) are distinguished by the ring structure of their mod 2-cohomology.

Equivariant Principal Bundles Over Spheres and Cohomogeneity One Manifolds

We classify smooth

The Walker conjecture for chains in ℝd.

{\rm SO}(n)

A limit of toric symplectic forms that has no periodic Hamiltonians

-equivariant principal bundles over

Cohomology rings of symplectic cuts

S^n

Conjugation spaces and edges of compatible torus actions

in terms of their isotropy representations over the north and south poles. This is an example of a general result classifying equivariant

Equivariant Bundles and Isotropy Representations

(\Pi, G)

Miscellaneous Applications and Developments

-bundles over manifolds with cohomogeneity 1.

Singular and Cellular (Co)homologies

A chain is a configuration in ℝd of segments of length l1, . . ., ln−1 consecutively joined to each other such that the resulting broken line connects two given points at a distance ln. For a fixed generic set of length parameters the space of all chains in ℝd is a closed smooth manifold of dimension (n − 2)(d − 1) − 1. In this paper we study cohomology algebras of spaces of chains. We give a complete classification of these spaces (up to equivariant diffeomorphism) in terms of linear inequalities of a special kind which are satisfied by the length parameters l1, . . ., ln. This result is analogous to the conjecture of K. Walker which concerns the special case d=2.