相关论文: Ping-Pong on Negatively Curved Groups
In the present note, we generalize the first part of the Borel-Cantelli lemma. By this generalization, we obtain some strong limit results.
Let $p \geq 5$ be a prime number. We find all the possible subgroups $G$ of ${\rm GL}_2 ( \mathbb{Z} / p \mathbb{Z} )$ such that there exists a number field $k$ and an elliptic curve ${\mathcal{E}}$ defined over $k$ such that the ${\rm Gal}…
In this work we carry out a complete group classification of Burgers' equations.
The goal of this note is to generalize Isoperimetric Inequality for random groups to the class of non-planar diagrams of bounded number of faces.
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 determine all the possible torsion groups of elliptic curves over cyclic cubic fields, over non-cyclic totally real cubic fields and over complex cubic fields.
In this short note, we prove a formula for the group inverse of a block matrix and consider the pseudo principal pivot transform expressed in terms of group inverses. Extensions of the usual principal pivot transform, where the usual…
We discuss upper and lower bounds for the size of gaps in the length spectrum of negatively curved manifolds. For manifolds with algebraic generators for the fundamental group, we establish the existence of exponential lower bounds for the…
We define the notion of a negatively curved tangent bundle of a metric measured space. We prove that, when a group $G$ acts on a metric measured space $X$ with a negatively curved tangent bundle, then $G$ acts on some $L^p$ space, and that…
This book provides a self-contained introduction to geometric group theory. The topics range from an introduction of Cayley and Schreier graphs to Gromov's theorem on groups of polynomial growth and amenability. We discuss the ping-pong…
In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie…
We give an elementary proof of the reducedness of twisted loop groups along the lines of the Kneser-Tits problem.
In this note I give a positive solution to Bullett's conjecture (posed in [1]) regarding a geometric presentation of the universal mod $p$ oriented ring spectrum.
We adapt the Ping-Pong Lemma, which historically was used to study free products of groups, to the setting of the homeomorphism group of the unit interval. As a consequence, we isolate a large class of generating sets for subgroups of…
It is well known that many famous Burnside-type problems have positive solutions for PI-groups and PI-algebras. In the present article we also consider various Burnside-type problems for PI-groups and PI-representations of groups.
We prove the ergodic Closing Lemma for Nonsingular Endomorphisms.
In this paper, we generalise results obtained earlier by John Cremona and the author on the reduction theory of binary forms, which describe positive zero-cycles in P^1, to positive zero-cycles (or point clusters) in projective spaces of…
We introduce the notion of a Lie superheaps as a generalisation of Lie supergroups. We show that the well-known `groupification' and `heapification' functors generalise to the ambience of supergeometry. In particular, we show that there is…
The use of geometric invariants has recently played an important role in the solution of classification problems in non-commutative ring theory. We construct geometric invariants of non-commutative projectivizations, a significant class of…
We use classical results in smoothing theory to extract information about the rational homotopy groups of the space of negatively curved metrics on a high dimensional manifold. It is also shown that smooth M-bundles over spheres equipped…