Related papers: Relating the Farrell Nil-groups to the Waldhausen …

We prove a 2-categorical analogue of a classical result of Drinfeld: there is a one-to-one correspondence between connected, simply-connected Poisson Lie 2-groups and Lie 2-bialgebras. In fact, we also prove that there is a one-to-one…

We prove the vanishing of bounded cohomology with separable dual coefficients for many groups of interest in geometry, dynamics, and algebra. These include compactly supported structure-preserving diffeomorphism groups of certain manifolds;…

First and second fundamental theorems are given for polynomial invariants of a class of pseudo-reflection groups (including the Weyl groups of type $B_n$), under the assumption that the order of the group is invertible in the base field.…

The descent method is one of the approaches to study the Brauer--Manin obstruction to the local--global principle and to weak approximation on varieties over number fields, by reducing the problem to ``descent varieties''. In recent lecture…

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 classify the finite primitive permutation groups which have a cyclic subgroup with two orbits. This extends classical topics in permutation group theory, and has arithmetic consequences. By a theorem of C. L. Siegel, affine algebraic…

A toric polyhedron is a reduced closed subscheme of a toric variety that are partial unions of the orbits of the torus action. We prove vanishing theorems for toric polyhedra. We also give a proof of the $E_1$-degeneration of Hodge to de…

The main objective of this paper is to determine the simplicial and cyclic cohomology groups of the Cuntz semigroup algebra $\ell^1(\Cuntz)$. In order to do so, we first establish some general results which can be used when studying…

Schur rings over the infinite dihedral group $\mathcal{Z}\rtimes\mathcal{Z}_2$ are studied according to properties of Schur rings over infinite groups and the classification of Schur rings over infinite cyclic groups. Schur rings over…

Let $\mathbb{F}_\ell$ be a finite field with $\ell$ elements and let $G = C_p \rtimes C_m$ be a faithful split metacyclic group. In this paper, we develop a complete theory for the twisted group algebra $\mathbb{F}_\ell^\alpha G$. Using the…

This paper contains the results of my PhD-thesis. I will show the K- and L-theoretic Farrell-Jones conjecture (FJC) for the general linear groups over the rationals and over the rational functions over a finite field. This especially…

We study the residual Eisenstein cohomology of semisimple groups in the context of maximal parabolic subgroups which remain maximal over $\mathbb{R}$. Under certain general hypotheses, we show that these residual representations are…

We study intersection theoretic problems in the setting of Chow-Witt groups with coefficients in a fixed Milnor-Witt cycle algebra over a perfect field. We prove that the product maps on such groups satisfy the following property: given two…

We show that the holomorph of the free group on two generators satisfies the Farrell-Jones Fibered Isomorphism Conjecture. As a consequence, we show that the lower K-theory of the above group vanishes.

We discuss a conjecture which says that the automorphism group of the Weyl algebra in characteristic zero is canonically isomorphic to the automorphism group of the corresponding Poisson algebra of classical polynomial symbols. Several…

We generalize a theorem of Tate and show that the second cohomology of the Weil group of a global or local field with coefficients in $\C^*$ (or more generally, with coefficients in the complex points of a tori over $\C$) vanish, where the…

We use a simple geometric argument and small cancellation properties of link groups to prove that alternating links are non-trivial. This proof uses only classic results in topology and combinatorial group theory.

Consider a pseudogroup on (C,0) generated by two local diffeomorphisms having analytic conjugacy classes a priori fixed in Diff(C,0). We show that a generic pseudogroup as above is such that every point has (possibly trivial) cyclic…

We show that except in several cases conjugacy classes of classical Weyl groups $W(B_n)$ and $W(D_n)$ are of type {\rm D}. We prove that except in three cases Nichols algebras of irreducible Yetter-Drinfeld ({\rm YD} in short )modules over…

We investigate two ways in which self-maps of an infinite set may be close to bijections; our investigation generates a $\mathbb{Z}$-valued index theory and a corresponding extension by $\mathbb{Z}$ for the quotient of the full symmetric…