Tautness and applications of the Alexander-Spanier cohomology of -types.
Tensor products of categories of equivariant perverse sheaves
Tetrahedra on deformed spheres and integral group cohomology.
The 3-cocycles of the Alexander quandles .
The abelianization of the Johnson kernel
We prove that the first complex homology of the Johnson subgroup of the Torelli group is a non-trivial, unipotent -module for all and give an explicit presentation of it as a -module when . We do this by proving that, for a finitely generated group satisfying an assumption close to formality, the triviality of the restricted characteristic variety implies that the first homology of its Johnson kernel is a nilpotent module over the corresponding Laurent polynomial ring, isomorphic to the...
The Bar Spectral Sequence converging to h*(SO(2n+1)).
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 Boardman category of spectra, chain complexes and (co)-localizations.
The Boolean algebra of spectra.
The chromatic -term for .
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 algebra of certain free loop spaces
Let X be a simply connected space and LX the space of free loops on X. We determine the mod p cohomology algebra of LX when the mod p cohomology of X is generated by one element or is an exterior algebra on two generators. We also provide lower bounds on the dimensions of the Hodge decomposition factors of the rational cohomology of LX when the rational cohomology of X is a graded complete intersection algebra. The key to both of these results is the identification of an important subalgebra of...
The cohomology algebras of orientable Seifert manifolds and applications to Lusternik-Schnirelmann category
This note gives a complete description of the cohomology algebra of any orientable Seifert manifold with ℤ/p coefficients, for an arbitrary prime p. As an application, the existence of a degree one map from an orientable Seifert manifold onto a lens space is completely determined. A second application shows that the Lusternik-Schnirelmann category for a large class of Seifert manifolds is equal to 3, which in turn is used to verify the Ganea conjecture for these Seifert manifolds.
The cohomology of holomorphic self maps of the Riemann sphere.
The Cohomology of the Morava Stabilizer Algebras.
The complex of words and Nakaoka stability.
The connective K-theory of spinor groups.
We study the properties of the connective K-theory with Z2 coefficients of the Lie groups Spin(n). This generalises some work by L. Hodgkin.
The cyclic groups and the free loop space.
The cyclic homology of p-adic reductive groups.
The cyclotomic trace and algebraic K-theory of spaces.