Related papers: $\mathcal{Z}$-compactifiable manifolds which are n…

In this paper we obtain a complete characterization of pseudo-collarable $n$-manifolds for $n\geq 6$. This extends earlier work by Guilbault and Tinsley to allow for manifolds with noncompact boundary. In the same way that their work can be…

In 1976, Chapman and Siebenmann \cite{CS76} established necessary and sufficient conditions for $\mathcal{Z}$-compactifying Hilbert cube manifolds. While these conditions are known to be necessary for a manifold $M^n$ to admit a…

We gather in this note results and examples about collared or non-collared boundaries of non-metrisable manifolds. Almost everything is well known but a bit scattered in the literature, and some of it is apparently not published at all.

We give a simple construction of new, complete, finite volume manifolds $M$ of bounded, nonpositive curvature. These manifolds have ends that look like a mixture of locally symmetric ends of different ranks and their fundamental groups are…

We demonstrate the existence of quasiconformal mappings on closed manifolds that cannot be decomposed as a composition of mappings with arbitrarily small conformal distortion.

We study computable topological spaces and semicomputable and computable sets in these spaces. In particular, we investigate conditions under which semicomputable sets are computable. We prove that a semicomputable compact manifold $M$ is…

A semi-computable set S in a computable metric space need not be computable. However, in some cases, if S has certain topological properties, we can conclude that S is computable. It is known that if a semi-computable set S is a compact…

We continue our study of ends non-compact manifolds. The over-arching aim is to provide an appropriate generalization of Siebenmann's famous collaring theorem that applies to manifolds having non-stable fundamental group systems at…

Recently, Zhang \cite{Zh20} and Li-Su-Wang-Zhang \cite{LSWZ24+} generalized Llarull's theorem to the noncompact complete spin manifold. In this paper, we further extend their results to the noncompact manifold with compact boundary.

We investigate conditions under which a co-computably enumerable closed set in a computable metric space is computable and prove that in each locally computable computable metric space each co-computably enumerable compact manifold with…

This paper is concerned with "nice" compactifications of manifolds. Siebenmann's iconic dissertation characterized open manifolds M^m (m>5) compactifiable by addition of a manifold boundary. His theorem extends easily to cases where M^m is…

Let $Z$ be a non-compact two-dimensional manifold and $\Delta$ be a one-dimensional foliation of $Z$ such that $\partial Z$ consists of leaves of $\Delta$ and each leaf of $\Delta$ is a non-compact closed subset of $Z$. We obtain a…

We investigate whether non-metrizable manifolds in various classes can be homotopy equivalent to a CW-complex (in short: heCWc), and in particular contractible. We show that a non-metrizable manifold cannot be heCWc if it has one of the…

Let F be a foliation of codimension 2 on a compact manifold with at least one non-compact leaf. We show that then F must contain uncountably many non-compact leaves. We prove the same statement for oriented p-dimensional foliations of…

It is presented an example of a holomorphic foliation of a non-algebraizable surface which is topologically equivalent to an algebraic foliation.

For a class of non compact Riemannian manifolds with ends, we give pseudo-differential expansions of bounded functions of the semi-classical Laplacian and study related Lp boundedness properties.

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

We construct examples of (effective) closed orbifolds which are covered by manifolds, but not finitely so.

We continue our study of ends of non-compact manifolds, with a focus on the inward tameness condition. For manifolds with compact boundary, inward tameness, has significant implications. For example, such manifolds have stable homology at…

We present a family of examples of two dimensional, hyperbolic complex manifolds whose envelopes of holomorphy are not hyperbolic.