Related papers: Classifying foliations
Several approaches were proposed to describe the geomorphology of drainage networks and the abiotic/biotic factors determining their morphology. There is an intrinsic complexity of the explicit qualification of the morphological variations…
In this note we define fibrations of topological stacks and establish their main properties. We prove various standard results about fibrations (fiber homotopy exact sequence, Leray-Serre and Eilenberg-Moore spectral sequences, etc.). We…
We classify weighted forests up to the blowing-up and blowing-down operations which are relevant for the study of algebraic surfaces.
In this article, we first describe codimension two regular foliations with numerically trivial canonical class on complex projective manifolds whose canonical class is not numerically effective. Building on a recent algebraicity criterion…
FlowClass.jl is a Julia package for classifying continuous-time dynamical systems into a hierarchy of structural classes: Gradient, Gradient-like, Morse-Smale, Structurally Stable, and General. Given a vector field…
There are a least uncountably many diffeomorphism types for open manifolds. Hence the classification problem is extremely difficult. We proceed as follows: We define several uniform structures of proper metric spaces and consider their arc…
We investigate the $\mathcal F$-Borel complexity of topological spaces in their different compactifcations. We provide a simple proof of the fact that a space can have arbitrarily many different complexities in different compactifications.…
Following Losik's approach to Gelfand's formal geometry, certain characteristic classes for codimension-one foliations coming from the Gelfand-Fuchs cohomology are considered. Sufficient conditions for non-triviality in terms of dynamical…
The theory of twistors on foliated manifolds is developed and the twistor space of the normal bundle is constructed. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate…
We introduce a combinatorial model based on measured foliations in surfaces which captures the phenomenology of open/closed string interactions. The predicted equations are derived in this model, and new equations can be discovered as well.…
These are the lecture notes based on earlier papers with some additional new results. New and simple proofs are given for local freeness theorem and the semipositivity theorem. A decomposition theorem for higher direct images of dualizing…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
Lindel\"of spaces are studied in any basic Topology course. However, there are other interesting covering properties with similar behaviour, such as almost Lindel\"of, weakly Lindel\"of, and quasi-Lindel\"of, that have been considered in…
We describe notions of tautness that arise in the study of $C^0$ foliations, $C^{1,0}$ or smoother foliations, and in geometry. We give examples to show that these notions are different, and discuss how these differences impact some…
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…
Second-order polynomials generalize classical first-order ones in allowing for additional variables that range over functions rather than values. We are motivated by their applications in higher-order computational complexity theory,…
The experiments conducted by various scientific groups indicate that, in dense two-dimensional systems of elongated particles subjected to vibration, the pattern formation is possible. Computer simulations have evidenced that the random…
We describe dynamical properties of a map $\mathfrak{F}$ defined on the space of rational functions. The fixed points of $\mathfrak{F}$ are classified and the long time behavior of a subclass is described in terms of Eulerian polynomials.
We construct partial category-valued field theories in (2+1)-dimensions using Lagrangian Floer theory in moduli spaces of central-curvature unitary connections with fixed determinant of rank r and degree d where r,d are coprime positive…
A dual foliation treatment of General Relativity is presented. The basic idea of the construction is to consider two foliations of a spacetime by spacelike hypersurfaces and relate the two geometries. The treatment is expected to be useful…