-homotopy and refinement of observation. II: Adding new -homotopy equivalences.
Tautness and applications of the Alexander-Spanier cohomology of -types.
Taylor towers for -modules
We consider Taylor approximation for functors from the small category of finite pointed sets to modules and give an explicit description for the homology of the layers of the Taylor tower. These layers are shown to be fibrant objects in a suitable closed model category structure. Explicit calculations are presented in characteristic zero including an application to higher order Hochschild homology. A spectral sequence for the homology of the homotopy fibres of this approximation is provided.
Taylor towers of symmetric and exterior powers
We study the Taylor towers of the nth symmetric and exterior power functors, Spⁿ and Λⁿ. We obtain a description of the layers of the Taylor towers, and , in terms of the first terms in the Taylor towers of and for t < n. The homology of these first terms is related to the stable derived functors (in the sense of Dold and Puppe) of and . We use stable derived functor calculations of Dold and Puppe to determine the lowest nontrivial homology groups for and .
Teisi in .
Tensor products of categories of equivariant perverse sheaves
Tensor products of spectra and localizations.
Teorema de Gauss-Bonnet para fíbrados de Seifert.
Tetrahedra on deformed spheres and integral group cohomology.
The ℤ₂-cohomology cup-length of real flag manifolds
Using fiberings, we determine the cup-length and the Lyusternik-Shnirel’man category for some infinite families of real flag manifolds , q ≥ 3. We also give, or describe ways to obtain, interesting estimates for the cup-length of any , q ≥ 3. To present another approach (combining well with the “method of fiberings”), we generalize to the real flag manifolds Stong’s approach used for calculations in the ℤ₂-cohomology algebra of the Grassmann manifolds.
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 algebraic topology of smooth algebraic varieties
The Anosov theorem for infranilmanifolds with an odd-order Abelian holonomy group.
The asymptotic dimension of the first Grigorchuk group is infinity.
We describe a sufficient condition for a finitely generated group to have infinite asymptotic dimension. As an application, we conclude that the first Grigorchuk group has infinite asymptotic dimension.
The Bar Spectral Sequence converging to h*(SO(2n+1)).
The based SU(n)-instanton moduli spaces.
The Batalin-Vilkovisky Algebra on Hochschild Cohomology Induced by Infinity Inner Products
We define a BV-structure on the Hochschild cohomology of a unital, associative algebra with a symmetric, invariant and non-degenerate inner product. The induced Gerstenhaber algebra is the one described in Gerstenhaber’s original paper on Hochschild-cohomology. We also prove the corresponding theorem in the homotopy case, namely we define the BV-structure on the Hochschild-cohomology of a unital -algebra with a symmetric and non-degenerate -inner product.
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.