Related papers: Residually free 3-manifolds

This paper uses Brin and Thickstun's theory of end reductions of non-compact 3-manifolds to study groups of covering translations of irreducible contractible open 3-manifolds W which are not homeomorphic to R^3. We associate to W an object…

For $\Sigma$ an orientable surface of finite topological type having genus at least 3 (possibly closed or possibly with any number of punctures or boundary components), we show that the mapping class group $Mod(\Sigma)$ has no faithful…

A (quasi-)Hamiltonian manifold is called multiplicity free if all of its symplectic reductions are 0-dimensional. In this paper, we classify multiplicity free Hamiltonian actions for (twisted) loop groups or, equivalently, multiplicity free…

The question in the title, first raised by Goldman and Donaldson, was partially answered by Reznikov. We give a complete answer, as follows: if G can be realized as both the fundamental group of a closed 3-manifold and of a compact K\"ahler…

We show that Out(G) is residually finite if G is a one-ended group that is hyperbolic relative to virtually polycyclic subgroups. More generally, if G is one-ended and hyperbolic relative to proper residually finite subgroups, the group of…

Let M be a Riemannian n-manifold with n greater than or equal to 3. For k between 1 and n, we say M has k-positive Ricci curvature if at every point of M the sum of any k eigenvalues of the Ricci curvature is strictly positive. In…

A topological space is called self-covering if it is a nontrivial cover of itself. We prove that a closed self-covering manifold $M$ with free abelian fundamental group fibers over a circle under certain assumptions. In particular, we give…

Computations based on explicit 4-periodic resolutions are given for the cohomology of the finite groups G known to act freely on S^3, as well as the cohomology rings of the associated 3-manifolds (spherical space forms) M = S^3/G. Chain…

We give upper bounds on the numbers of various classes of polynomials reducible over the integers and over integers modulo a prime and on the number of matrices in SL(n), GL(n) and Sp(2n) with reducible characteristic polynomials, and on…

We study ruled submanifolds of Euclidean space. First, to each (parametrized) ruled submanifold $\sigma$, we associate an integer-valued function, called degree, measuring the extent to which $\sigma$ fails to be cylindrical. In particular,…

A residually nilpotent group is \emph{$k$-parafree} if all of its lower central series quotients match those of a free group of rank $k$. Magnus proved that $k$-parafree groups of rank $k$ are themselves free. We mimic this theory with…

Let $\mathcal M (\Sigma, \mathcal P)$ be the mapping class group of a punctured oriented surface $(\Sigma, \mathcal P)$ (where $\mathcal P$ may be empty), and let $\mathcal T_p(\Sigma,\mathcal P)$ be the kernel of the action of $\mathcal M…

Associated to every complete affine 3-manifold M with nonsolvable fundamental group is a noncompact hyperbolic surface S. We classify such complete affine structures when Sigma is homeomorphic to a three-holed sphere. In particular, for…

This paper investigates conditions under which a given automorphism of a residually torsion-free nilpotent group respects some ordering of the group. For free groups and surface groups, this has relevance to ordering the fundamental groups…

Given a compact Riemannian manifold with boundary, we prove that the space of embedded, which may be improper, free boundary minimal hypersurfaces with uniform area and Morse index upper bound is compact in the sense of smoothly graphical…

We show that a complete contractible 3-manifold with positive scalar curvature and bounded geometry must be $\mathbb R^3$. We also show that an open handlebody of genus larger than 1 does not admit complete metrics with positive scalar…

Adyan and Rabin showed that most properties of groups cannot be algorithmically recognized from a finite presentation alone. We prove that, if one is also given a solution to the word problem, then the class of fundamental groups of closed,…

We show that if a sequence $M_n$ of closed aspherical $d$-dimensional Riemannian manifolds with Ricci curvature uniformly bounded below and diameter uniformly bounded above collapses, then for all large enough $n$, the fundamental groups…

We investigate the manifold $\cal{M}$ of (real) quadratic forms in n > 1 variables having a multiple eigenvalue. In addition to known facts, we prove that 1) $\cal{M}$ is irreducible, 2) in the case of n = 3, scalar matrices and only them…

We prove that there are infinitely many pairwise non-commensurable hyperbolic $n$-manifolds that have the same ambient group and trace ring, for any $n \geq 3$. The manifolds can be chosen compact if $n \geq 4$.