Related papers: Overlays and group actions
Since the time when the first optical instruments have been invented, an idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way to formalize it in mathematics is…
An envelope in a category is a construction that generalizes the operations of "exterior completion", like completion of a locally convex space, or Stone-\v{C}ech compactification of a topological space, or universal enveloping algebra of a…
We establish new characterizations for (pseudo)isometric extensions of topological dynamical systems. For such extensions, we also extend results about relatively invariant measures and Fourier analysis that were previously only known in…
Graphings are special bounded-degree graphs on probability spaces, representing limits of graph sequences that are convergent in a local or local-global sense. We describe a procedure for turning the underlying space into a compact metric…
Complex networks topologies present interesting and surprising properties, such as community structures, which can be exploited to optimize communication, to find new efficient and context-aware routing algorithms or simply to understand…
Application-level peer-to-peer (P2P) network overlays are an emerging paradigm that facilitates decentralization and flexibility in the scalable deployment of applications such as group communication, content delivery, and data sharing.…
We introduce a new topological invariant of complex line arrangements in the complex projective plane, derived from the interaction between their complement and the boundary of a regular neighbourhood. The motivation is to identify Zariski…
Our main result states that for each finite complex L the category ${\bf TOP}$ of topological spaces possesses a model category structure (in the sense of Quillen) whose weak equivalences are precisely maps which induce isomorphisms of all…
Hypergraphs, a generalization of graphs, naturally represent groupwise relationships among multiple individuals or objects, which are common in many application areas, including web, bioinformatics, and social networks. The flexibility in…
Given a closed orientable surface (\Sigma) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (\Sigma) and the convex compact set of additive functions on…
In this paper, using the classical covering theory, we introduce a generalization of covering maps of a space $X$ with respect to a topology $\tau$ on the fundamental group of $X$. We show that the famous notions, covering, semicovering,…
The notion of overlap algebra introduced by G. Sambin provides a constructive version of complete Boolean algebra. Here we first show some properties concerning overlap algebras: we prove that the notion of overlap morphism corresponds…
Let X and Y be curves over a finite field. In this article we explore methods to determine whether there is a rational map from Y to X by considering L-functions of certain covers of X and Y and propose a specific family of covers to…
A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties…
Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group…
We study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph to…
A partial group is a generalization of the concept of group recently introduced by A. Chermak. By considering partial groups as simplicial sets, we propose an extension theory for partial groups using the concept of (simplicial) fibre…
Let $G$ be a graph and $f: G\rightarrow G$ be a continuous map. We establish a structure theorem which describes the structures of the set $R(f)-\overline{P(f)}$, where $R(f)$ and $P(f)$ are the recurrent point set and the periodic point…
In this paper, we present a constructive and proof-relevant development of graph theory, including the notion of maps, their faces, and maps of graphs embedded in the sphere, in homotopy type theory. This allows us to provide an elementary…
We introduce orbifolds from the classical point of view, using charts, and present orbifold versions of elementary objects from Algebraic Topology, such as the fundamental group, coverings and Euler characteristic; Differential…