The geometry of a vector bundle endowed with a cone field.
The geometry of configuration spaces for closed chains in two and three dimensions.
The geometry of the local cohomology filtration in equivariant bordism.
The homology of some groups of diffeomorphisms.
The integral cohomology algebras of ordered configuration spaces of spheres.
The integral cohomology rings of real infinite-dimensional flag manifolds
The Lenstra map on classifying spaces and G-theory of group rings.
The level of real projective spaces.
The Lyusternik-Shnirel'man category, vector bundles, and immersions of manifolds.
The Mod 2 Cohomology Rings of Extra-special 2-groups and the Spinor Groups.
The Mumford conjecture
The Mumford Conjecture asserts that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra on the Mumford-Morita-Miller characteristic classes; this can be reformulated in terms of the classifying space derived from the mapping class groups. The conjecture admits a topological generalization, inspired by Tillmann’s theorem that admits an infinite loop space structure after applying Quillen’s plus construction. The text presents the proof by Madsen and...
The non-criticality of certain families of affine varieties.
The order of the Hopf bundle on projective Stiefel manifolds
The Positvity of the Chern Classes of an Ample Vector Bundle.
The rational homotopy of Thom spaces and the smoothing of homology classes.
The rational homotopy type of configuration spaces of two points
We prove that the rational homotopy type of the configuration space of two points in a -connected closed manifold depends only on the rational homotopy type of that manifold and we give a model in the sense of Sullivan of that configuration space. We also study the formality of configuration spaces.
The real K-ring of some CW-complexes of small dimension
The ring of upper triangular invariants as a module over the Dickson invariants.
The Salvetti complex and the little cubes
For a real central arrangement , Salvetti introduced a construction of a finite complex Sal which is homotopy equivalent to the complement of the complexified arrangement in [Sal87]. For the braid arrangement , the Salvetti complex Sal serves as a good combinatorial model for the homotopy type of the configuration space of points in , which is homotopy equivalent to the space of k little -cubes. Motivated by the importance of little cubes in homotopy theory, especially in the study of...
The Signature mod 8