Higher-dimensional categories with finite derivation type.
Hochschild cohomology of complex spaces and Noetherian schemes.
Hochschild homology of finite dimensional algebras.
Hodge decomposition for higher order Hochschild homology
Homological algebra and divergent series.
Homological Algebra of Novikov-Shubin Invariants and Morse Inequalities.
Homological Criteria for Finiteness.
Homological Dimension of Pullbacks.
Homological dimensions and approximate contractibility for Köthe algebras
We give a survey of our recent results on homological properties of Köthe algebras, with an emphasis on biprojectivity, biflatness, and homological dimension. Some new results on the approximate contractibility of Köthe algebras are also presented.
Homological methods in the solution of certain functional equations.
Homological perturbation theory and associativity.
Homological projective duality
We introduce a notion of homological projective duality for smooth algebraic varieties in dual projective spaces, a homological extension of the classical projective duality. If algebraic varieties X and Y in dual projective spaces are homologically projectively dual, then we prove that the orthogonal linear sections of X and Y admit semiorthogonal decompositions with an equivalent nontrivial component. In particular, it follows that triangulated categories of singularities of these sections are...
Homologie cyclique, caractère de Chern et lemme de perturbation.
Homologie cyclique, principe de Selberg et pseudo-coefficient.
Homologie cyclique : rapport sur des travaux récents de Connes, Karoubi, Loday, Quillen...
Homologie de Frobenius.
Homologie de l'algèbre quantique des symboles pseudo-différentiels sur le cercle
Homologie et modèle minimal des algèbres de Gerstenhaber
On étudie ici les notions d’algèbre de Gerstenhaber à homotopie près et d’homologie des algèbres de Gerstenhaber du point de vue de la théorie des opérades. Précisément, on donne une description explicite des -algèbres à homotopie près (c’est-à-dire d’algèbres sur le modèle minimal de l’opérade des algèbres de Gerstenhaber). On décrit également le complexe calculant l’homologie des -algèbres. On donne une suite spectrale qui converge vers cette homologie et quelques exemples de calculs. Enfin...
Homology and modular classes of Lie algebroids
For a Lie algebroid, divergences chosen in a classical way lead to a uniquely defined homology theory. They define also, in a natural way, modular classes of certain Lie algebroid morphisms. This approach, applied for the anchor map, recovers the concept of modular class due to S. Evens, J.-H. Lu, and A. Weinstein.
Homology fibrations and “group-completion” revisited.