Related papers: Bypass attachments in higher-dimensional contact t…
We study contact posets and show that every contact poset can be embedded into a Boolean poset with overlap contact relation. Contact posets and (nonadditive) contact semilattices have the superamalgamation property, Fra\"\i ss\'e limits…
Consider the topologically enriched category of compact smooth manifolds (possibly with corners), with morphisms given by codimension zero smooth embeddings. Now formally identify any object X with its thickening X x [-1,1]. We prove that…
Higher order anisotropic superspaces are constructed as generalized vector superbundles provided with compatible nonlinear connection, distinguished connection and metric structures.
We continue the study of intersection bodies of polytopes, focusing on the behavior of $IP$ under translations of $P$. We introduce an affine hyperplane arrangement and show that the polynomials describing the boundary of $I(P+t)$ can be…
In recent times a great amount of progress has been achieved in symplectic and contact geometry, leading to the development of powerful invariants of 3-manifolds such as Heegaard Floer homology and embedded contact homology. These…
In this paper, a Riemannian geometry of noncommutative super surfaces is developed which generalizes [4] to the super case. The notions of metric and connections on such noncommutative super surfaces are introduced and it is shown that the…
The main theme of this paper is the dynamics of Reeb flows with symmetries on the standard contact sphere. We introduce the notion of strong dynamical convexity for contact forms invariant under a group action, supporting the standard…
Overlap functions were introduced as class of bivariate aggregation functions on [0, 1] to be applied in image processing. This paper has as main objective to present appropriates definitions of overlap functions considering the scope of…
Interference detection of arbitrary geometric objects is not a trivial task due to the heavy computational load imposed by implementation issues. The hierarchically structured bounding boxes help us to quickly isolate the contour of…
A geometric obstruction, the so called "plastikstufe", for a contact structure to not being fillable has been found by K. Niederkruger. This generalizes somehow the concept of overtwisted structure to dimensions higher than 3. This paper…
We introduce a modification procedure for Engel structures that is reminiscent of the Lutz twist in 3-dimensional Contact Topology. This notion allows us to define what an Engel overtwisted disc is, and to prove a complete h-principle for…
The realization of topological states of matter in ultracold atomic gases is currently the subject of intense experimental activity. Using a synthetic dimension, encoded in a non-spatial degree of freedom, can greatly simplify the…
We present a survey of the many and various elements of the modern higher-dimensional theory of quasiconformal mappings and their wide and varied application. It is unified (and limited) by the theme of the author's interests. Thus we will…
We consider the standard Darboux space equipped with the radial symmetric contact form. We study co-orientation preserving contactomorphisms between relatively compact domains up to the boundary. We determine the contactomorphism classes…
In this article we show that in any dimension there exist infinitely many pairs of formally contact isotopic isocontact embeddings into the standard contact sphere which are not contact isotopic. This is the first example of rigidity for…
Motivated by recent theoretical and experimental interest in metamaterials comprising non-local coupling terms, we present an analytic framework to realise materials with arbitrary complex dispersion relations. Building on the inverse…
The tight span, or injective envelope, is an elegant and useful construction that takes a metric space and returns the smallest hyperconvex space into which it can be embedded. The concept has stimulated a large body of theory and has…
We develop the theory of multiplicative Ehresmann connections for Lie groupoid submersions covering the identity, as well as their infinitesimal counterparts. We construct obstructions to the existence of such connections, and we prove…
Relativistic phase space distributions are very interesting objects as they allow one to gather the information extracted from various types of experiments into a single coherent picture. Focusing on the four-dimensional transverse phase…
In recent years, there has been a surge of interest in higher-order topological phases (HOTPs) across various disciplines within the field of physics. These unique phases are characterized by their ability to harbor topological protected…