Related papers: On Burghelea Conjecture
We review the Burghelea conjecture, which constitutes a full computation of the periodic cyclic homology of complex group rings, and its relation to the algebraic Baum-Connes conjecture. The Burghelea conjecture implies the Bass conjecture.…
We establish the Hodge conjecture for the top dimensional cohomology group with integer coefficients of any $q$-complete complex manifold $X$ with $q<\dim X$. This holds in particular for the complement $X=\mathbb{C}\mathbb{P}^n\setminus A$…
We completely determine cohomology groups of sections of homogeneous line bundles over a toroidal group.
We construct a finitely generated group that does not satisfy the generalized Burghelea conjecture.
We prove the Baum-Connes conjecture for hyperbolic groups and their subgroups.
We prove some basic facts on parahoric subgroups and on Iwahori-Weyl groups.
We prove the Carlson-Toledo conjecture (for all Kahler groups which do not have property T of Kazhdan).We deduce a conjecture of Goldman-Donaldson for all 3-manifold groups which are rich in the sense of [Re2].
We present some new results on the cohomology of a large scope of SL\_2-groups in degrees above the virtual cohomological dimension; yielding some partial positive results for the Quillen conjecture in rank one. We combine these results…
We propose a new refinement of the McKay conjecture and we prove it for symmetric groups.
In this article, we introduce the first degrees of a cochain complex associated to a strict Lie 2-group whose cohomology is shown to extend the classical cohomology theory of Lie groups. In particular, we show that the second cohomology…
In this paper, we prove the K- and L-theoretical Isomorphism Conjecture for Baumslag-Solitar groups with coefficients in an additive category.
In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.
Computations in the cohomology of finite groups.
Provides a counterexample to a long standing conjecture of A. Adem regarding the behaviour of the integral cohomology of a p-group.
In this article, we introduce a new cohomology theory associated to a Lie 2-algebras. This cohomology theory is shown to extend the classical cohomology theory of Lie algebras; in particular, we show that the second cohomology group…
We give a new proof of the Mordell-Lang conjecture in positive characteristic for finitely generated subgroups. We also make some progress towards the full Mordell-Lang conjecture in positive characteristic.
We provide new sufficient conditions under which Ryser's conjecture holds.
We generalise to profinite groups some of our previous results on the cohomology of pro-p groups of bounded sectional p-rank.
In this article we study the homology of nilpotent groups. In particular a certain vanishing result for the homology and cohomology of nilpotent groups is proved.
We prove the A-theoretic Isomorphism Conjecture with coefficients and finite wreath products for solvable groups.