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Simplicial algebra, homology theories, K- theory and homotopy theory

Objective

The project is centered around simplicial algebra and topology, (co)homology theories, algebraic K-theory and cobordism. It is intended to make progress on the Karoubi conjecture, to develop further the interrelation between algebraic K-theory, bivariant K-theory and equivariant homology of groups, to construct and develop the non- abelian cohomology of crossed structures; another goal is to construct and study the n-fold Cech cohomology of open covers and the n-fold Cech derived factors of group valued factors.

A second aspect of the program is to produce new information on the multiplicative structure of the simplectic cobordism ring, to give presentations of Morava K-theory and Brown-Peterson cohomology of p-groups in terms of transferred Chern classes, to get new calculations for elliptic cohomology for toric manifolds, and to obtain the analog of the Birman Ko Lee presentation for singular braid monoid.

The third aspect is to find conditions of triviality for the second L_p-cohomology of discrete groups with applications to noncompact manifolds, to obtain analogues to the Davis-Okun theories for right-angled Coxeter groups, to determine the homotopy type of embedding spaces of manifolds. Related to K-theory and Hochschild cohomology
one wants computations of the Gerstenhaber algebra on the homology of the free loop space.

One wants to make a significant contribution towards the proof of the Milnor-Friedlander conjecture, to prove the rigidity of the Henselian case for all cohomologies represented by a T-spectrum, to calculate cohomology of Steinberg groups modeled on Chevalley groups.

The last aspect of the program concerns explicit computations of primary cyclic and Hochschild homologies for commutative algebras, applications to representation theory of algebras, developing the foundation of the theory of exact couples in Raikov-semiabelian categories, and the study of the global properties of certain functor categories : the so called "artinian conjecture" as well as their Gabriel-Krull filtration.

Coordinator

Université Paris 13
Address
Av. J. B. Clément 90
93430 Villetaneuse
France

Participants (6)

Georgian Academy of Sciences A.Razmadze Mathematical Institute
Georgia
Address
M. Alexidze 1
0193 Tbilisi
Siberian Branch of the RAS Sobolev Institute of Mathematics
Russia
Address
Akademik Koptyug Prospect 4
630090 Novosibirsk
St. Petersburg State University
Russia
Address
Gorohovaya 36-47
191023 St. Petersburg
University Montpellier 2
France
Address
Place Eugene Bataillon
34095 Montpellier
University of Glasgow
United Kingdom
Address
University Gardens 12
G12 8QW Glasgow
Université Catholique de Louvain
Belgium
Address
Chemin Du Cyclotron
1348 Louvain La Neuve