Related papers: Aspherical groups and manifolds with extreme prope…

We show that the aspherical manifolds produced via the relative strict hyperbolization of polyhedra enjoy many group-theoretic and topological properties of open finite volume negatively pinched manifolds, including relative hyperbolicity,…

The main subjects of the paper is studying the fundamental groups of closed symplectically aspherical manifolds. Motivated by some results of Gompf, we introduce two classes of fundamental groups $\pi_1(M)$ of symplectically aspherical…

We classify the possible elementary amenable fundamental groups of compact aspherical 4-manifolds with boundary and conclude that they are either polycyclic or solvable Baumslag- Solitar. Since these groups are good and satisfy the…

This is a survey on known results and open problems about closed aspherical manifolds, i.e., connected closed manifolds whose universal coverings are contractible. Many examples come from certain kinds of non-positive curvature conditions.…

We show that in all dimensions >7 there are closed aspherical manifolds whose fundamental groups have nontrivial center but do not possess any topological circle actions. This disproves a conjectured converse (proposed by Conner and…

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 study noncompact, complete, finite volume, Riemannian 4-manifolds $M$ with sectional curvature $-1<K<0$. We prove that $\pi_1 M$ cannot be a 3-manifold group. A classical theorem of Gromov says that $M$ is homeomorphic to the interior of…

We construct examples of complete quaternionic K\"ahler manifolds with an end of finite volume, which are not locally homogeneous. The manifolds are aspherical with fundamental group which is up to an infinite cyclic extension a semi-direct…

We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively…

We undertake a systematic investigation of compact aspherical manifolds with boundary; motivated by the plethora of examples in the bounded case and by the beauty of the theory in the closed case. Our main theorems give a homological…

We show that a space with a finite asymptotic dimension is embeddable in a non-positively curved manifold. Then we prove that if a uniformly contractible manifold X is uniformly embeddable in $\R^n$ or non-positively curved n-dimensional…

In this article, we prove that the fundamental group $\pi_1(M)$ of a complete open manifold $M$ with nonnegative Ricci curvature is finitely generated, under the condition that the Riemannian universal cover $\tilde M$ satisfies an "almost…

Main Theorem (3.3): Let $M$ be a compact four-dimensional manifold either with curvature, positive on complex isotropic two-planes, or self-dual of positive scalar curvature. If $\pi_1 (M)$ admits a nontrivial unitary representation, and…

For each nonnegative integer m we show that any closed, oriented topological four-manifold with fundamental group Z_{4m+2} and odd intersection form, with possibly seven exceptions, either admits no smooth structure or admits infinitely…

We define a new class of irreducible groups, called groups not infinite-index presentable by products or not IIPP. We prove that certain aspherical manifolds with fundamental groups not IIPP do not admit maps of non-zero degree from direct…

We show that the fundamental group of every enumeratively rationally connected closed symplectic manifold is finite. In other words, if a closed symplectic manifold has a non-zero Gromov-Witten invariant with two point insertions, then it…

We prove that a closed $n$-manifold $M$ with positive scalar curvature and abelian fundamental group admits a finite covering $M'$ which is strongly inessential. The latter means that a classifying map $u:M'\to K(\pi_1(M'),1)$ can be…

Let $M$ be a 4-dimensional open manifold with nonnegative Ricci curvature. In this paper, we prove that if the universal cover of $M$ has Euclidean volume growth, then the fundamental group $\pi_1(M)$ is finitely generated. This result…

We give examples of closed, oriented 3-manifolds whose fundamental groups are not isomorphic, but yet have the same sets of finite quotient groups; hence the same profinite completions. We also give examples of compact, oriented 3-manifolds…

We investigate asymptotically flat manifolds with cone structure at infinity. We show that any such manifold M has a finite number of ends. For simply connected ends we classify all possible cones at infinity, except for the 4-dimensional…