Related papers: The triangulation of manifolds

Some geometric structures with associated Riemannian metrics have been considered in the book.

There are many open problems and some mysteries connected to the realizations of the associahedra as convex polytopes. In this note, we describe three -- concerning special realizations with the vertices on a sphere, the space of all…

In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…

It is known that any two triangulations of a compact 3-manifold are related by finite sequences of certain local transformations. We prove here an upper bound for the length of a shortest transformation sequence relating any two…

This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete…

This is an expository and introductory note on some results obtained in "Coisotropic embeddings in Poisson manifolds" (ArXiv math/0611480). Some original material is contained in the last two sections, where we consider linear Poisson…

We propose some problems on the classification of toric manifolds from the viewpoint of topology and survey related results.

An unfolding of a polyhedron along its edges is called a vertex unfolding if adjacent faces are allowed to be connected at not only an edge but also a vertex. Demaine et al showed that every triangulated polyhedron has a vertex unfolding.…

We present several problems and results relating the scalar curvatures of manifolds with mean curvatures of their boundaries

In this article we establish the relation between the spines of 3-manifolds and the polyhedra with identified faces. We do this by showing that the spines of the closed, connected, orientable 3-manifolds can be presented through polyhedra…

This is a problem list in the theory of foliations and laminations of 3-manifolds. The focus is on the relationship of foliations and laminations with other aspects of 3-manifold topology, especially with the Thurston theory of geometric…

A mixture of an historical article, and of a survey of recent developments, containing also a couple of new results.

In this expository paper, we present a survey about the history of the geometrization conjecture and the background material on the classification of Thurston's eight geometries. We also discuss recent techniques for immersive visualization…

We study the large-scale geometry of 3-manifolds with nontrivial 2-dimensional bounded cohomology, with a view to proving a weak version of the geometrization conjecture for such manifolds.

In the theory of configuration spaces, "splitting" usually refers to the phenomenon that the configuration spaces on a manifold and those on its punctured version are closely related cohomologically. We prove a splitting theorem that is…

A notion of general manifolds is introduced. It covers all usual manifolds in mathematics. Essentially, it is a way how to get a bigger 'fibration' over a site which locally coincides with a given one. An enrichment with generalized…

We discuss intuitive ideas and historical background of concepts in the analysis on configurations with singularities, here in connection with our iterative approach for higher singularities.

This is a chapter (planned to appear in Wiley's upcoming Encyclopedia of Operations Research and Management Science) describing parts of the theory of convex polyhedra that are particularly important for optimization. The topics include…

A pseudo-triangle is a simple polygon with three convex vertices, and a pseudo-triangulation is a face-to-face tiling of a planar region into pseudo-triangles. Pseudo-triangulations appear as data structures in computational geometry, as…

We state a number of open questions on 3-dimensional Poincar\'e duality groups and their subgroups, motivated by considerations from 3-manifold topology.