Related papers: The geography problem for 4-manifolds with specifi…

It is well-known that there are 19 classes of geometries for 4-dimensional manifolds in the sense of Thurston. We could ask that to what extent the geometric information is revealed by the profinite completion of the fundamental group of a…

There are only 10 Euclidean forms, that is flat closed three dimensional manifolds: six are orientable and four are non-orientable. The aim of this paper is to describe all types of $n$-fold coverings over orientable Euclidean manifolds…

A 4-dimensional Riemannian manifold equipped with an endomorphism of the tangent bundle, whose fourth power is the identity, is considered. The matrix of this structure in some basis is circulant and the structure acts as an isometry with…

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…

Let $ 1 \rightarrow N \rightarrow G \rightarrow Q \rightarrow 1$ be an exact sequence of finitely presented groups where Q is infinite and not virtually cyclic, and is the fundamental group of some closed 3-manifold. If G is Kaehler, we…

Even though the disk embedding theorem is not available in dimension 4 for free fundamental groups, some surgery problems may be shown to have topological solutions. We prove that surgery problems may be solved if one considers closed…

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…

This survey paper is devoted to Riemannian manifolds with special holonomy. To any Riemannian manifold of dimension n is associated a closed subgroup of SO(n), the holonomy group; this is one of the most basic invariants of the metric. A…

For every N > 0 there exists a group of deficiency less than -N that arises as the fundamental group of a smooth homology 4-sphere and also as the fundamental group of the complement of a compact contractible submanifold of the 4-sphere. A…

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 discuss the geography problem of closed oriented 4-manifolds that admit a Riemannian metric of positive scalar curvature, and use it to survey mathematical work employed to address Gromov's observation that manifolds with positive scalar…

This is a summary of some of the basic facts about flat 2-orbifold groups, otherwise known as 2-dimensional crystallographic groups. We relate the geometric and topological presentations of these groups, and consider structures…

We prove that every finitely generated group with recursive aspherical presentation embeds into a group with finite aspherical presentation. This and several known facts about groups and manifolds imply that there exists a 4-dimensional…

Let $\pi$ be a group satisfying the Farrell-Jones conjecture and assume that $B\pi$ is a 4-dimensional Poincar\'e duality space. We consider topological, closed, connected manifolds with fundamental group $\pi$ whose canonical map to $B\pi$…

A compact oriented 4-manifold is defined to be of ``superconformal simple type'' if certain polynomials in the basic classes (constructed using the Seiberg-Witten invariants) vanish identically. We show that all known 4-manifolds of…

We classify topological $4$-manifolds with boundary and fundamental group $\mathbb{Z}$, under some assumptions on the boundary. We apply this to classify surfaces in simply-connected $4$-manifolds with $S^3$ boundary, where the fundamental…

We prove that the minimal Euler characteristic of a closed symplectic four-manifold with given fundamental group is often much larger than the minimal Euler characteristic of almost complex closed four-manifolds with the same fundamental…

We prove two results relating 3-manifold groups to fundamental groups occurring in complex geometry. Let N be a compact, connected, orientable 3-manifold. If N has non-empty, toroidal boundary, and \pi_1(N) is a Kaehler group, then N is the…

We prove that on closed Riemannian manifolds with infinite abelian, but not cyclic, fundamental group, any isometry that is homotopic to the identity possesses infinitely many invariant geodesics. We conjecture that the result remains true…

In 2018, M. Chu and S. Tillmann gave a lower bound for the trisection genus of a closed 4-manifold in terms of the Euler characteristic of $M$ and the rank of its fundamental group. We show that given a group $G$, there exist a 4-manifold…