Related papers: Ping-Pong on Negatively Curved Groups
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
We consider the logic space of countable (enumerated) groups and show that closed subspaces corresponding to some standard classes of groups have (do not have) generic groups. We also discuss the cases of semigroups and associative rings.
In this article we formulate a version of the analytic Novikov conjecture for semigroups rather than groups, and show that the descent argument from coarse geometry generalises effectively to this new situation.
In this note, we give examples that demonstrate a negative answer to the generalized numerical criterion problem for pairs.
A new generalization of the classical separate algebraicity theorem is suggested and proved.
We present a rather general version of the snake lemma for abelian groups.
The group ring of the automorphism group of a p-group is studied using the automorphism groups of subgroups and quotient groups of P.
The aim of the present paper is to study the distributions of the length multiplicities for negatively curved locally symmetric Riemannian manifolds. In Theorem 2.1, we give upper bounds of the length multiplicities and the square sums of…
We give a new proof of Quillen's conjecture for solvable groups via a geometric and explicit method. For p-solvable groups, we provide both a new proof using the Classification of Finite Simple Groups and an asymptotic version without…
We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic. The methods we develop apply to a broad class of connected linear algebraic groups defined over finite fields…
We develop techniques for classifying the nonnegatively curved left-invariant metrics on a compact Lie group G. We prove rigidity theorems for general G and a partial classification for G=SO(4). Our approach is to reduce the general…
A regularity lemma for polynomials provides a decomposition in terms of a bounded number of approximately independent polynomials. Such regularity lemmas play an important role in numerous results, yet suffer from the familiar shortcoming…
In this paper, we prove a generalization of Geraghty's fixed point theorem for multi--valued mappings.
We prove that the enumerative polynomials of generalized Stirling permutations by the statistics of plateaux, descents and ascents are partial $\gamma$-positive. Specialization of our result to the Jacobi-Stirling permutations confirms a…
We prove a combination theorem for hyperbolic groups, in the case of groups acting on complexes displaying combinatorial features reminiscent of non-positive curvature. Such complexes include for instance weakly systolic complexes and…
We prove moving lemma for additive higher Chow groups of smooth projective varieties. As applications, we prove the very general contravariance property of additive higher Chow groups. Using the moving lemma, we establish the structure of…
We show that certain aspherical manifolds arising from hyperplane arrangements in negatively curved manifolds have relatively hyperbolic fundamental group.
We develop the theory of group graded division ring parallel to the one by P. Cohn for (ungraded) division rings.
We compute the $L^p$-cohomology spaces of some negatively curved manifolds. We deal with two cases: manifolds with finite volume and sufficiently pinched negative curvature, and conformally compact manifolds.
We demonstrate how a generic automated theorem prover can be applied to establish the non-orderability of groups. Our approach incorporates various tools such as positive cones, torsions, generalised torsions and cofinal elements.