Related papers: A separable non-remainder of H

Let G be a finitely generated linear group over a field of characteristic 0. Suppose that every solvable subgroup of G is polycyclic. Then the claim is made that any solvable subgroup of G is separable. This is proven for G=SL_n(Z).…

In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.

It is shown that there exist $\mathcal{Z}$-compactifiable manifolds with noncompact boundary which fail to be pseudo-collarable.

We show that Keisler's order is not linear, assuming the existence of a supercompact cardinal.

An example is given of a divisor of a curve which is not a trace divisor of a foliation.

The moduli spaces of theta-semistable representations of a finite quiver can be packaged together to form a noncommutative compact manifold.

We consider a separable compact line $K$ and its extension $L$ consisting of $K$ and a countable number of isolated points. The main object of study is the existence of a bounded extension operator $E: C(K)\to C(L)$. We show that if such an…

Let $f$ be a transcendental entire function. The escaping set $I(f)$ consists of those points that tend to infinity under iteration of $f$. We show that $I(f)$ is not $\sigma$-compact, resolving a question of Rippon from 2009.

A locally compact stable plane of positive topological dimension will be called semiaffine if for every line $L$ and every point $p$ not in $L$ there is at most one line passing through $p$ and disjoint from $L$. We show that then the plane…

We present an alternative proof of the following fact: the hyperspace of compact closed subsets of constant width in $\mathbb R^n$ is a contractible Hilbert cube manifold. The proof also works for certain subspaces of compact convex sets of…

We give examples of compactly supported Hamiltonian loops with non zero Calabi invariant on certain open symplectic manifolds.

We prove that any finite set of real numbers can be split into two parts, one part being highly non-additive and the other highly non-multiplicative.

Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space L(H) of linear bounded operators on H with weak operator topology. We prove that if U is a measurable map from G to L(H) then it…

We prove the Invariant Subspace Conjecture for separable Hilbert spaces.

We prove that there is a second countable locally compact group that does not embed as a closed subgroup in any compactly generated locally compact group, and discuss various related embedding and non-embedding results.

Let G be a second countable, locally compact group and let f be a continuous Herz-Schur multiplier on G. Our main result gives the existence of a (not necessarily uniformly bounded) strongly continuous representation on a Hilbert space,…

We show that it is consistent that the continuum is as large as you wish, and for each uncountable cardinal $\kappa$ below the continuum, there are a subset $T$ of the reals and a family $A$ of countable subsets of $T$ such that (1) both…

Over each nontrivial finite group $G$, there exists a finite system of equations having no solutions in larger finite groups but having a solution in a periodic group containing $G$. We prove several similar facts about amenable, orderable,…

Assuming the Continuum Hypothesis, there is a compact first countable connected space of weight aleph_1 with no totally disconnected perfect subsets. Each such space, however, may be destroyed by some proper forcing order which does not add…

We study the stability of non compact steady and expanding gradient Ricci solitons. We first show that strict linear stability implies dynamical stability. Then we give various sufficient geometric conditions ensuring the strict linear…