Related papers: Quantization of branched coverings

Branched covers of the complex projective line ramified over $0,1$ and $\infty$ (Grothendieck's {\em dessins d'enfant}) of fixed genus and degree are effectively enumerated. More precisely, branched covers of a given ramification profile…

In the present paper continuing our previous work we prove an extension theorem for matrices with entries in the algebra of bounded holomorphic functions defined on an unbranched covering of a Caratheodory hyperbolic Riemann surface of…

We consider *-linear maps into a commutative C*-algebra C (X) of continuous functions on a locally compact Hausdorff space X with certain specified properties and prove two results: (1) an extension result for a class of *-linear maps Y -->…

We define a new algebra of noncommutative differential forms for any Hopf algebra with an invertible antipode. We prove that there is a one to one correspondence between anti-Yetter-Drinfeld modules, which serve as coefficients for the Hopf…

We consider the union of certain irreducible components of cohomological support loci of the canonical bundle, which we call standard. We prove a structure theorem about them and single out some particular cases, recovering and improving…

In this paper we develop analysis of the monopole maps over the universal covering space of a compact four manifold. We induce a property on local properness of the covering monopole map under the condition of closeness of the AHS complex.…

Generalizing the notion of continuous Hilbert space representations of compact topological groups we define unitary continuous correpresentations of $C^*$-completions of compact quantum group Hopf algebras on arbitrary Hilbert spaces. It is…

For a finite tensor category $\mathcal C$ and a Hopf monad $T:\mathcal C\to \mathcal C$ satisfying certain conditions we describe exact indecomposable left $\mathcal C^T$-module categories in terms of left $\mathcal C$-module categories and…

The concept of quantization consists in replacing commutative quantities by noncommutative ones. In mathematical language an algebra of continuous functions on a locally compact topological space is replaced with a noncommutative…

Classes of branched surfaces extend the classes of surfaces or 2-dimensional manifolds satisfying suitable properties and defined in various manners. Reeb spaces of smooth maps of suitable classes into surfaces whose codimensions are…

Let $Conf^{lf}_{\infty}(\C)$ and $C^{lf}_{\infty}(\C)$ denote the locally finite infinite ordered and unordered configuration spaces of the complex plane. We prove that both $Conf^{lf}_{\infty}(\C)$ and $C^{lf}_{\infty}(\C)$ are aspherical.…

Let $p:\Sigma'\to\Sigma$ be a finite Galois cover, possibly branched, with Galois group $G$. We are interested in the structure of the cohomology of $\Sigma'$ as a module over $G$. We treat the cases of branched and unbranched covers…

We define branching systems for finitely aligned higher-rank graphs. From these we construct concrete representations of higher-rank graph C*-algebras on Hilbert spaces. We prove a generalized Cuntz-Krieger uniqueness theorem for periodic…

In this article, we will define non-commutative covering spaces using Hopf-Galois theory. We will look at basic properties of covering spaces that still hold for these non-commutative analogues. We will describe examples including coverings…

The goal of the present paper is to extend the theory of frames for countably generated Hilbert $C^*$-modules over arbitrary $C^*$-algebras. In investigating the non-unital case we introduce the concept of outer frame as a sequence in the…

Let $f: X \to Y$ be a regular covering of a surface $Y$ of finite type with nonempty boundary, with finitely-generated (possibly infinite) deck group $G$. We give necessary and sufficient conditions for an integral homology class on $X$ to…

We propose a generalization of the topological vertex, which we call the "non-commutative topological vertex". This gives open BPS invariants for a toric Calabi-Yau manifold without compact 4-cycles, where we have D0/D2/D6-branes wrapping…

We study the general structure of 2-C*-categories closed under conjugation, projections and direct sums. We do not assume units to be simple, i.e. for i_A the 1-unit corresponding to an object A, the space Hom(i_A, i_A) is a commutative…

The pro-algebraic fundamental group can be understood as a completion with respect to finite-dimensional non-commutative algebras. We introduce finer invariants by looking at completions with respect to Banach and C*-algebras, from which we…

This article introduces Hilbert $*$-categories: an abstraction of categories with similar algebraic and analytic properties to the categories of real, complex, and quaternionic Hilbert spaces and bounded linear maps. Other examples include…