Related papers: A combinatorial negative curvature condition imply…

Using a generalization of complexes, called 2-complexes, this paper defines and analyzes new Sobolev spaces of matrix fields and their interrelationships within a commuting diagram. These spaces have very weak second-order derivatives. An…

We give a complete characterization of the locally compact groups that are non-elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting…

The purpose of this note is to show that the regular locus of a complex variety is locally parabolic at the singular set. This yields that the regular locus of a compact complex variety, e.g., of a projective variety, is parabolic. We give…

We prove that under certain combinatorial conditions, the realization spaces of line arrangements on the complex projective plane are connected. We also give several examples of arrangements with eight, nine and ten lines which have…

The study of infinitesimal deformations of a variety embedded in projective space requires that of deformations of a collection of points, as specified by a zero-dimensional scheme. Further, basic problems in infinitesimal interpolation…

We develop a tighter implementation of basic PL topology, which keeps track of some combinatorial structure beyond PL homeomorphism type. With this technique we clarify some aspects of PL transversality and give combinatorial proofs of a…

We give an explicit expression for the contact loci of hyperplane arrangements and show that their cohomology rings are combinatorial invariants. We also give an expression for the restricted contact loci in terms of Milnor fibers of…

The paper surveys some new results and open problems connected with such fundamental combinatorial concepts as polytopes, simplicial complexes, cubical complexes, and subspace arrangements. Particular attention is paid to the case of…

From Smyth's classification, modular compactifications of pointed smooth rational curves are indexed by combinatorial data, so-called extremal assignments. We explore their combinatorial structures and show that any extremal assignment is a…

We show that a cosmological negative spatial curvature can account for both a recently identified phenomenological imprint of the global Hubble flow on galactic rotation curves and for the recently detected cosmic repulsion and cosmic…

This paper addresses weak approximation for rationally connected varieties defined over the function field of a curve, especially at places of bad reduction. Our approach entails analyzing the rational connectivity of the smooth locus of…

We introduce the notion of commability between locally compact groups, namely the equivalence relation generated by cocompact inclusions and quotients by compact normal subgroups. We give a classification of focal hyperbolic locally compact…

Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus…

Let $H$ be a group acting on a simply-connected diagrammatically reducible combinatorial 2-complex $X$ with fine 1-skeleton. If the fixed point set $X^ H$ is non-empty, then it is contractible. Having fine 1-skeleton is a weaker version of…

We study four-dimensional simplicial gravity through numerical simulation with special attention to the existence of singular vertices, in the strong coupling phase, that are shared by abnormally large numbers of four-simplices. We attempt…

We introduce combinatorial types of arrangements of convex bodies, extending order types of point sets to arrangements of convex bodies, and study their realization spaces. Our main results witness a trade-off between the combinatorial…

For each strongly connected finite-dimensional (pure) simplicial complex we construct a finite group, the group of projectivities of the complex, which is a combinatorial but not a topological invariant. This group is studied for…

Given a hyperbolic quadric of PG(5,2), there are 28 points off this quadric and 56 lines skew to it. It is shown that the $(28_6, 56_3)$-configuration formed by these points and lines is isomorphic to the combinatorial Grassmannian of type…

As an extension of the recent construction of generalised Fayet-Iliopoulos terms in ${\cal N}=1$ supergravity given in [1], we present self-interactions for a vector multiplet coupled to conformal supergravity. They are used to construct…

The closed string model in the background gravity field is considered as the bi-Hamiltonian system in assumption that string model is the integrable model for particular kind of the background fields. The dual nonlocal Poisson brackets, de…