Related papers: Unions of Cockroft two-complexes

Complex systems consist of interacting units whose interactions may be pairwise, involving two units, or higher-order, involving more than two units simultaneously. Graphs capture pairwise interactions and represent such systems as…

Cumulants are a notion that comes from the classical probability theory, they are an alternative to a notion of moments. We adapt the probabilistic concept of cumulants to the setup of a linear space equipped with two multiplication…

It is shown that an ensemble of particles with tripolar (colour) charges will necessarily cohere in a hierarchy of structures, from simple clusters and strings to complex aggregates and cyclic molecule-like structures. The basic…

We give characterizations of the center, of conjugated and of commuting elements in a fundamental group of a graph of group. We deduce various results : on the one hand we give a sufficient condition for the center, the centralizers, and…

The Darboux theorem in symplectic geometry implies that any two points in a connected symplectic manifold have neighbourhoods symplectomorphic to each other. The impossibility of such a theorem in the more general multisymplectic framework…

In the papers from Chui and Parnes (1971) and Luh (1972), as well on the paper from V.Nestoridis (1996) on the Universal Taylor series, it is used, without proof, that the union of two compact sets in $\mathbb{R} ^2$ with connected…

We present some ideas for a possible Noncommutative Floer Homology. The geometric motivation comes from an attempt to build a theory which applies to practically every 3-manifold (closed, oriented and connected) and not only to homology…

The "simplicial complexes" and "join" (*) today used within combinatorics aren't the classical concepts, cf. Spanier (1966) p. 108-9, but, exept for \emptyset, complexes having {\emptyset} as a subcomplex resp. \Sigma1 * \Sigma2 := {\sigma1…

Given a relation $R \subseteq I \times J$ between two sets, Dowker's Theorem (1952) states that the homology groups of two associated simplicial complexes, now known as Dowker complexes, are isomorphic. In its modern form, the full result…

Necessary and sufficient conditions for a finite connected graph with a strict partial order on vertices to be a combinatorial invariant of pseudoharmonic function are obtained.

We prove the Weinstein conjecture for non-trivial contact connected sums under either of two topological conditions: non-trivial fundamental group or torsion-free homology.

Using a new technique, we prove a rich family of special cases of the matroid intersection conjecture. Roughly, we prove the conjecture for pairs of tame matroids which have a common decomposition by 2-separations into finite parts.

We present a mathematical framework for describing the topology of configuration spaces for particles on one-connected graphs. In particular, we compute the homology groups over integers for different classes of one-connected graphs. Our…

We review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of $x-y$ dualities in a broader context of log…

We introduce the notion of matched pairs of Courant algebroids and give several examples arising naturally from complex manifolds, holomorphic Courant algebroids, and certain regular Courant algebroids. We consider the matched sum of two…

This chapter sets out preliminaries for the duality theory in later chapters. An underlying idea is that local cohomology functors are higher derived functors of colocalizations (a.k.a.~coreflections). Predominantly well-known facts about…

We reduce a strong version of the twist conjecture for Artin groups to Artin groups whose defining graphs have no separating vertices. This produces new examples of Artin groups satisfying the conjecture, and sheds more light on the…

We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.

In \cite{1}, a class of gyrogroups $(G,\odot)$ has been associated to certain groups $(G,\cdot)$. We give a necessary and sufficient condition for $(G,\odot)$ to be gyrocommutative. We also prove that under a suitable assumption two finite…

We survey interactions between the topology and the combinatorics of complex hyperplane arrangements. Without claiming to be exhaustive, we examine in this setting combinatorial aspects of fundamental groups, associated graded Lie algebras,…