Homological Criteria for Finiteness.
Homological fixed point theorems
Homological Methods and the Third Dimension Subgroup
Homological Methods Applied to the Derived Series of Groups
Homological methods in the solution of certain functional equations.
Homological Properties of Certain Arithmetic Groups in the Function Field Case.
Homological stability for automorphism groups of free groups.
Homologie du groupe linéaire et polylogarithmes
Homology and derived series of groups.
Homology and Direct Sums of Countable Abelian Groups.
Homology computations for complex braid groups
Complex braid groups are the natural generalizations of braid groups associated to arbitrary (finite) complex reflection groups. We investigate several methods for computing the homology of these groups. In particular, we get the Poincaré polynomial with coefficients in a finite field for one large series of such groups, and compute the second integral cohomology group for all of them. As a consequence we get non-isomorphism results for these groups.
Homology cylinders and the acyclic closure of a free group.
Homology groups and eight-term exact sequences
Homology of braid groups and their generalizations
In the paper we give a survey of (co)homologies of braid groups and groups connected with them. Among these groups are pure braid groups and generalized braid groups. We present explicit formulations of some theorems of V. I. Arnold, E. Brieskorn, D. B. Fuks, F. Cohen, V. V. Goryunov and others. The ideas of some proofs are outlined. As an application of (co)homologies of braid groups we study the Thom spectra of these groups.
Homology of classical Lie groups made discrete, I. Stability theorems and Schur mulipliers.
Homology of gaussian groups
We describe new combinatorial methods for constructing explicit free resolutions of by -modules when is a group of fractions of a monoid where enough lest common multiples exist (“locally Gaussian monoid”), and therefore, for computing the homology of . Our constructions apply in particular to all Artin-Tits groups of finite Coexter type. Technically, the proofs rely on the properties of least common multiples in a monoid.
Homology of -fold groupoids.
Homology of origamis with symmetries
Given an origami (square-tiled surface) with automorphism group , we compute the decomposition of the first homology group of into isotypic -submodules. Through the action of the affine group of on the homology group, we deduce some consequences for the multiplicities of the Lyapunov exponents of the Kontsevich-Zorich cocycle. We also construct and study several families of interesting origamis illustrating our results.
Homology of the Infinite Orthogonal and Symplectic Groups over Algebraically Closed Fields.
Homology of the Steinberg variety and Weyl group coinvariants.