Related papers: Kakutani-von Neumann maps on simplexes

We provide a new efficient diagrammatic tool, in the context of the scattering equations, for computation of covariant $D$-dimensional tree-level $n$-point amplitudes with pairs of spinning massive particles using compact exponential…

We study the space $Q_n$ of all configurations of $n$ ordered points on the circle such that no three points coincide, and in which one of the points (say, the last one) is fixed. We compute its fundamental group for $n<6$ and describe its…

We describe the inverse image of the Riemannian exponential map at a basepoint of a compact symmetric space as the disjoint union of so called focal orbits through a maximal torus. These are orbits of a subgroup of the isotropy group acting…

We reconstruct all (2+1)D quantum double models of finite groups from their boundary symmetries through the repeated application of a gauging procedure, extending the existing construction for abelian groups. We employ the recently proposed…

The commutative algebra of functions on a manifold is extended to a noncommutative algebra by considering its tensor product with the algebra of nxn complex matrices. Noncommutative geometry is used to formulate an extension of the…

Gauging introduces gauge fields in order to localize an existing global symmetry, resulting in a dual global symmetry on the gauge fields that can be gauged again. By iterating the gauging process on spin chains with Abelian group…

Substitution schemes provide a classical method for constructing tilings of Euclidean space. Allowing multiple scales in the scheme, we introduce a rich family of sequences of tile partitions generated by the substitution rule, which…

We classify parallelizable noncommutative manifold structures on finite sets of small size in the general formalism of framed quantum manifolds and vielbeins introduced previously. The full moduli space is found for $\le 3$ points, and a…

The Minkowski's Question-Mark function is a singular homeomorphism of the unit interval that maps the set of quadratic surds into the rationals. This function has deserved the attention of several authors since the beginning of the…

We establish an explicit formula for the Half-Wave maps equation for rational functions with simple poles. The Lax pair provides a description of the evolution of the poles. By considering a half-spin formulation, we use linear algebra to…

The harmonic sawtooth map w(x) of the unit interval onto itself is defined where it is shown that its fixed points are enumerated by generating functions involving the golden ratio in their parameters. The appropriately scaled Mellin…

(1) For a compact Riemannian manifold without boundary $(M,g)$ containing $n+1$ points $p_i$ and the $n$-dimensional standard simplex $\Delta$, the miniser of \[ E: M \times \Delta \to {\mathbf R}, (a,\lambda) \mapsto \lambda^0 d^2(a,p_0) +…

We study regular inclusions of finite-dimensional von Neumann algebras from a matrix-theoretic perspective. To this end, we introduce a new combinatorial invariant of an inclusion, called the normalizer matrix, which encodes the structure…

A generalization of the Choi-Jamiolkowski isomorphism for completely positive maps between operator algebras is introduced. Particular emphasis is placed on the case of normal unital completely positive maps defined between von Neumann…

Making use of its smooth structure only, out of a connected oriented smooth $4$-manifold a von Neumann algebra is constructed. It is geometric in the sense that is generated by local operators and as a special four dimensional phenomenon it…

This paper surveys the role of moment maps in K\"ahler geometry. The first section discusses the Ricci form as a moment map and then moves on to moment map interpretations of the K\"ahler--Einstein condition and the scalar curvature…

A rotation in a Euclidean space V is an orthogonal map on V which acts locally as a plane rotation with some fixed angle. We give a classification of all pairs of rotations in finite-dimensional Euclidean space, up to simultaneous…

Elements of a global operator approach to the WZWN theory for compact Riemann surfaces of arbitrary genus $g$ are given. Sheaves of representations of affine Krichever-Novikov algebras over a dense open subset of the moduli space of Riemann…

We establish the existence of new rigidity and rationality phenomena in the theory of nonabelian group actions on the circle, and introduce tools to translate questions about the existence of actions with prescribed dynamics into finite…

In this paper, we develop a loop group description of harmonic maps $\mathcal{F}: M \rightarrow G/K$ of finite uniton number, from a Riemann surface $M,$ compact or non-compact, into inner symmetric spaces of compact or non-compact type. As…