Related papers: A survey on quasiperiodic topology
A simple algebraic model for charged particle moving in two dimensional space under influence of singular magnetic field is given. The fundamental assumption for the model is that every charged particle coupled to the magnetic field is…
In 2001 E. Ghys, X. Gomez-Mont and J. Saludes defined the Fatou and Julia components of transversely holomorphic foliations on compact manifolds. It is a partition of the manifold in two saturated sets: the Fatou set which represents the…
The classification of one parameter local Coulomb branch solution of theories with eight supercharges is given by assuming that it is given by a genus $g$ fiberation of Riemann surfaces. The crucial point is the fact that certain conjugacy…
Let C be the class of compact 2n-dimensional symplectic manifolds M for which the first or (n-1) Chern class vanish. We point out an integer optimization problem to find a lower bound B(n) on the number of equilibrium points of…
We use quasimap Floer cohomology for varying symplectic quotients to resolve several puzzles regarding displaceability of toric moment fibers. For example, we (i) present a compact Hamiltonian torus action containing an {\em open} subset of…
A singular Riemannian foliation $F$ on a complete Riemannian manifold $M$ is called a polar foliation if, for each regular point $p$, there is an immersed submanifold $\Sigma$, called section, that passes through $p$ and that meets all the…
In this paper, we propose a class of quantum Markov fields QMF on a graphs $G= (V,E)$. The Markov structure of the considered QMF is investigated in the finer structure of a quasi-local algebrav $\mathcal{A}_V$ of observables based over a…
A smooth foliation is Riemannian when its leaves are locally equidistant. The closures of the leaves of a Riemannian foliation on a simply connected manifold, or more generally of a Killing foliation, are described by flows of transverse…
In the paper we develop a method to evaluate the topological degree of the Poincare map of the mathematical model of narrow lagoon subject to a T-periodic forcing. Using the method developved we arrive to the conditions for the parameteres…
Multilinear varieties, defined as the sets of rational points of varieties cut out by multilinear functions, were first introduced and studied by Gowers and Mili\'{c}evi\'{c}[Proc. Edinb. Math. Soc., 2021] for finite $\mathbb{K}$. In this…
In 1993, Bartnik introduced a quasi-spherical construction of metrics of prescribed scalar curvature on 3-manifolds. Under quasi-spherical ansatz, the problem is converted into the initial value problem for a semi-linear parabolic equation…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
We survey two decades of work on the (sequential) topological complexity of configuration spaces of graphs (ordered and unordered), aiming to give an account that is unifying, elementary, and self-contained. We discuss the traditional…
We study the topology of the space of smooth codimension one foliations on a closed 3-manifold. We regard this space as the space of integrable plane fields included in the space of all smooth plane fields. It has been known since the late…
The two function theories of monogenic and of slice monogenic functions have been extensively studied in the literature and were developed independently; the relations between them, e.g. via Fueter mapping and Radon transform, have been…
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
Vladimir Turaev discovered in the early years of quantum topology that the notion of modular category was an appropriate structure for building 3-dimensional Topological Quantum Field Theories (TQFTs for short) containing invariants of…
Let $G$ be a simple algebraic group over the complex field $\mathbb C$, $P$ a parabolic subgroup containing $B$ its Borel subgroup, $P'$ its derived group and $\mathfrak m$ the Lie algebra of its nilradical. The nilfibre $\mathscr N$ for…
In this letter we proved this theorem: \emph{if $F$ be a holomorphic mapping of $T_{\Omega}$ to a mapping manifold $X$ such that for every compact subset $K\subset \Omega$ the mapping $F$ is uniformly continues on $T_{K}$ and $F(T_{K})$ is…
We incorporate pearly Floer trajectories into the transversality scheme for pseudoholomorphic maps introduced by Cieliebak-Mohnke. By choosing generic domain-dependent almost complex structures we obtain zero and one-dimensional moduli…