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.
The cohomology ring of the Hilbert scheme of 3 points on a smooth projective variety.
The combinatorial formula of Gabrielov, Gelfand and Losik for the first Pontrjagin class
The compression theorem I.
The compression theorem II: directed embeddings.
The compression theorem III: Applications.
The computation of Stiefel-Whitney classes
The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here “compute” means to find a presentation in terms of generators and relations, and involves only the underlying (graded) ring. We propose a method to determine some of the extra structure: namely, Stiefel-Whitney classes and Steenrod operations. The calculations are explicitly carried out for about one hundred groups (the results can be consulted on the Internet).Next,...
The Contractibility of the Homeomorphism Group of Some Product Spaces by Wong's Method.
The cyclotomic trace and algebraic K-theory of spaces.
The diffeomorphism classification of non-simply connected Dolgachev surfaces.
The diffeomorphism group of a Lie foliation
We describe explicitly the group of transverse diffeomorphisms of several types of minimal linear foliations on the torus , . We show in particular that non-quadratic foliations are rigid, in the sense that their only transverse diffeomorphisms are and translations. The description derives from a general formula valid for the group of transverse diffeomorphisms of any minimal Lie foliation on a compact manifold. Our results generalize those of P. Donato and P. Iglesias for , P. Iglesias and...
The diffeomorphism group of a non-compact orbifold [Book]
The diffeomorphism group of a Riemannian foliation.
The dilatation invariant in the homotopy of spheres.
The directional dimension of subanalytic sets is invariant under bi-Lipschitz homeomorphisms
Let be a set-germ at such that . We say that is a direction of at if there is a sequence of points tending to such that as . Let denote the set of all directions of at .Let be subanalytic set-germs at such that . We study the problem of whether the dimension of the common direction set, is preserved by bi-Lipschitz homeomorphisms. We show that although it is not true in general, it is preserved if the images of and are also subanalytic. In particular if two subanalytic...
The discriminant and oscillation lengths for contact and Legendrian isotopies
We define an integer-valued non-degenerate bi-invariant metric (the discriminant metric) on the universal cover of the identity component of the contactomorphism group of any contact manifold. This metric has a very simple geometric definition, based on the notion of discriminant points of contactomorphisms. Using generating functions we prove that the discriminant metric is unbounded for the standard contact structures on and . On the other hand we also show by elementary arguments that the...
The Dynamical Complexity of Orientation Reversing Homeomorphisms of Surfaces.
The eta Invariant and ...O of Lens Spaces.