Displaying similar documents to “Trees of manifolds and boundaries of systolic groups”

Trees of manifolds with boundary

Paweł Zawiślak (2015)

Colloquium Mathematicae

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We introduce two new classes of compacta, called trees of manifolds with boundary and boundary trees of manifolds with boundary. We establish their basic properties.

Group-theoretic conditions under which closed aspherical manifolds are covered by Euclidean space

Hanspeter Fischer, David G. Wright (2003)

Fundamenta Mathematicae

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Hass, Rubinstein, and Scott showed that every closed aspherical (irreducible) 3-manifold whose fundamental group contains the fundamental group of a closed aspherical surface, is covered by Euclidean space. This theorem does not generalize to higher dimensions. However, we provide geometric tools with which variations of this theorem can be proved in all dimensions.

On stability of 3-manifolds

Sławomir Kwasik, Witold Rosicki (2004)

Fundamenta Mathematicae

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We address the following question: How different can closed, oriented 3-manifolds be if they become homeomorphic after taking a product with a sphere? For geometric 3-manifolds this paper provides a complete answer to this question. For possibly non-geometric 3-manifolds, we establish results which concern 3-manifolds with finite fundamental group (i.e., 3-dimensional fake spherical space forms) and compare these results with results involving fake spherical space...

Folner sets of alternate directed groups

Jérémie Brieussel (2014)

Annales de l’institut Fourier

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An explicit family of Folner sets is constructed for some directed groups acting on a rooted tree of sublogarithmic valency by alternate permutations. In the case of bounded valency, these groups were known to be amenable by probabilistic methods. The present construction provides a new and independent proof of amenability, using neither random walks, nor word length.

A short introduction to shadows of 4-manifolds

Francesco Costantino (2005)

Fundamenta Mathematicae

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We give a self-contained introduction to the theory of shadows as a tool to study smooth 3-manifolds and 4-manifolds. The goal of the present paper is twofold: on the one hand, it is intended to be a shortcut to a basic use of the theory of shadows, on the other hand it gives a sketchy overview of some of the most recent results on shadows. No original result is proved here and most of the details of the proofs are left out.

Products of open manifolds with ℝ

Craig R. Guilbault (2007)

Fundamenta Mathematicae

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We present a characterization of those open n-manifolds (n ≥ 5) whose products with the real line are homeomorphic to interiors of compact (n+1)-manifolds with boundary.

On Compact Complex Manifolds with Finite Automorphism Group

Konrad Czaja (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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It is known that compact complex manifolds of general type and Kobayashi hyperbolic manifolds have finite automorphism groups. We give criteria for finiteness of the automorphism group of a compact complex manifold which allow us to produce large classes of compact complex manifolds with finite automorphism group but which are neither of general type nor Kobayashi hyperbolic.