Related papers: Lyons Taming

Given two univalent harmonic mappings $f_1$ and $f_2$ on $\mathbb{D}$, which lift to minimal surfaces via the Weierstrass-Enneper representation theorem, we give necessary and sufficient conditions for $f_3=(1-s)f_1+sf_2$ to lift to a…

Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group SU(2). In this picture the group elements are represented by ``turns'', which are equivalence classes of directed great circle arcs…

We give the first examples of groups which admit a tame combing with linear radial tameness function with respect to any choice of finite presentation, but which are not minimally almost convex on a standard generating set. Namely, we…

We prove a Simons-type holonomy theorem for totally skew 1-forms with values in a Lie algebra of linear isometries. The only transitive case, for this theorem, is the full orthogonal group. We only use geometric methods and we do not use…

Article is devoted to the Examples 2 and 3 of the symplectic solvable Lie groups $R$ with some special cohomological properties, which have been constructed by Benson and Gordon. But they are not succeeded in constructing corresponding…

Let $G$ be a finite group, $N(G)$ be the set of conjugacy classes of the group $G$. In the present paper it is proved $G\simeq L$ if $N(G)=N(L)$, where $G$ is a finite group with trivial center and $L$ is a finite simple group of…

We describe the construction of a minimal presentation for the group of planar pure braids $\overline{P}_n$ on $n$ strands. The generators of this presentation are dual to the generators of the cohomology ring of $\overline{P}_n$ found by…

Let $G$ be an anisotropic semisimple group over a totally real number field $F$. Suppose that $G$ is compact at all but one infinite place $v_0$. In addition, suppose that $G_{v_0}$ is $\mathbb{R}$-almost simple, not split, and has a Cartan…

We prove that, provided $d > k$, every sufficiently large subset of $\mathbf{F}_q^d$ contains an isometric copy of every $k$-simplex that avoids spanning a nontrivial self-orthogonal subspace. We obtain comparable results for simplices…

We introduce a set of combinatorial techniques for studying the simplicial bounded cohomology of semi-simplicial sets, simplicial complexes and posets. We apply these methods to prove several new bounded acyclicity results for…

The aim of this paper is to give verifiable criteria for the existence of {\em irreducible} homomorphisms of $\pi_{1}(\mathbb P^1 - \mathcal R)$ into compact semisimple groups, for a finite subset $\mathcal R$ such that the conjugacy…

Our paper develops a theory of Poisson slices and a uniform approach to their partial compactifications. The theory in question is loosely comparable to that of symplectic cross-sections in real symplectic geometry.

Ulam asked whether all Lie groups can be represented faithfully on a countable set. We establish a reduction of Ulam's problem to the case of simple Lie groups. In particular, we solve the problem for all solvable Lie groups and more…

In this article we give an self contained existence proof for J. Conway's sporadic simple group Co_1 [4] using the second author's algorithm [14] constructing finite simple groups from irreducible subgroups of GL_n(2). Here n = 11 and the…

The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…

Let $F$ be a non-archimedean local field of odd residual characteristic. We compute the Jordan set of a simple cuspidal representation of a symplectic group over $F$, using explicit computations of generators of the Hecke algebras of covers…

A complete mapping of a group $G$ is a permutation $\phi:G\rightarrow G$ such that $g\mapsto g\phi(g)$ is also a permutation. Complete mappings of $G$ are equivalent to tranversals of the Cayley table of $G$, considered as a latin square.…

In the Labourie-Loftin parametrization of the Hitchin component of surface group representations into SL(3,R), we prove an asymptotic formula for holonomy along rays in terms of local invariants of the holomorphic differential defining that…

We prove an equivariant version of the local splitting theorem for tame Poisson structures and Poisson actions of compact Lie groups. As a consequence, we obtain an equivariant linearization result for Poisson structures whose transverse…

Recent work has shown that if an isostatic bar and joint framework possesses non-trivial symmetries, then it must satisfy some very simply stated restrictions on the number of joints and bars that are `fixed' by various symmetry operations…