-homotopy and refinement of observation. II: Adding new -homotopy equivalences.
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 spectra and localizations.
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 Boardman category of spectra, chain complexes and (co)-localizations.
The Boolean algebra of spectra.
The Borsuk homotopy extension theorem without the binormality condition
The cancellation problem for homotopy equivalent representations of finite groups: a survey
The center of a graded connected Lie algebra is a nice ideal
Let be a free graded connected differential Lie algebra over the field of rational numbers. An ideal in the Lie algebra is called nice if, for every cycle such that belongs to , the kernel of the map , , is contained in . We show that the center of is a nice ideal and we give in that case some informations on the structure of the Lie algebra . We apply this computation for the determination of the rational homotopy Lie algebra of a simply connected space . We deduce that the...
The Classification of Simply Connected H-Spaces with Three Cells II.
The Classification of Simply Connected H-Spaces with Three Cells I.
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 classifying space of the 1 + 1 dimensional cobordism category.
The closure of a model category
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 ring of free loop spaces.