Related papers: Topological properties of reflectionless canonical…
We study the topological components of the surface group representations into $\mathrm{SL}(2,\mathbb{R})$ and $\mathrm{PSL}(2,\mathbb{R})$. Utilizing the signature formula established in [14], we determine the number of connected components…
I am interested in canonical systems and Dirac operators that are reflectionless on an open set. In this situation, the half line $m$ functions are holomorphic continuations of each other and may be combined into a single function. By…
A canonical system of basic invariants is a system of invariants satisfying a set of differential equations. The properties of a canonical system are related to the mean value property for polytopes. In this article, we naturally identify…
In this paper we study the reflections of the category of topological and semitopological semigroups on the category of the class of topological spaces satisfying separation axioms $T_{0}$, $T_{1}$, $T_{2}$, $T_{3}$ and regular and we apply…
We define a class of insulators with gapless surface states protected from localization due to the statistical properties of a disordered ensemble, namely due to the ensemble's invariance under a certain symmetry. We show that these…
We develop a comprehensive theory of reflectionless canonical systems with an arbitrary Dirichlet-regular Widom spectrum with the Direct Cauchy Theorem property. This generalizes, to an infinite gap setting, the constructions of finite gap…
In this paper, we study the topological properties of five-dimensional rotating charged black holes in different ensembles.The topological numbers for the black holes are gotten in the grand canonical and canonical ensembles, which are 1.…
The central idea of metamaterials and metaoptics is that, besides their base materials, the geometry of structures offers a broad extra dimension to explore for exotic functionalities. Here, we discover that the topology of structures…
In this paper we complete the topological description of the space of representations of the fundamental group of a punctured surface in SL(2,R) with prescribed behavior at the punctures and nonzero Euler number, following the strategy…
In this article, we study the properties of the autonomous superposition operator on the space of formal power series, including those with nonzero constant term. We prove its continuity and smoothness with respect to the topology of…
We initiate the study of p-adic algebraic groups G from the stability-theoretic and definable topological-dynamical points of view, that is, we consider invariants of the action of G on its space of types over Q_p in the language of fields.…
We give a self-contained and enriched review about topology properties in the rapidly growing field of topological states of matter (TSM). This review is mainly focus on the beautiful interplay of topology mathematics and condensed matter…
The local topological properties of black hole systems can be expressed by the winding numbers as the defects. As so far, AdS black hole thermodynamics is often depicted by the dual parameters of $(T,S),~ (P,V), (\Phi, Q)$ in the extended…
We compute the mapping class group action on cycles on the configuration space of the torus with one puncture, with coefficients in a local system arising in conformal field theory. This action commutes with the topological action of the…
A Fock space is introduced that admits an action of a quantum group of type A supplemented with some extra operators. The canonical and dual canonical basis of the Fock space are computed and then used to derive the finite-dimenisonal…
Topological metals are special conducting materials with gapless band structures and nontrivial edge-localized resonances, whose discovery has proved elusive because the traditional topological classification methods do not apply in this…
We investigate hidden symmetries in minimally coupled scalar field cosmology within the FLRW universe, and a perfect fluid with and without interaction to the scalar field. We show that for an exponential potential there exists a set of…
The discreteness problem for finitely generated subgroups of $PSL(2,\mathbb{R})$ and $PSL(2,\mathbb{C})$ is a long-standing open problem. In this paper we consider whether or not this problem is decidable by an algorithm. Our main result is…
We investigate the topological properties of reflection zeros of three-layer structures consisting of a dielectric layer sandwiched between two metal layers, which can be used as optical differentiators. We show that the reflection zeros…
Using the isomorphism between highest weight U_q(sl_2)-modules and homologies of certain local systems on the configuration spaces, constructed by Varchenko, we give a geometric construction of the dual of the Lusztig's canonical basis in a…