Related papers: Dimers on surface graphs and spin structures. II

Let $\Gamma_g$ be the fundamental group of a closed connected orientable surface of genus $g\geq2$. We introduce a combinatorial structure of "core surfaces", that represent subgroups of $\Gamma_g$. These structures are (usually)…

Let $G$ be a Lie group, and let $(M,\omega)$ be a symplectic manifold. If $G$ admits a Hamiltonian action on $(M,\omega)$ with momentum map $\mu$, then $M$, the zero-level set of $\mu$, the orbit space, and the corresponding symplectic…

We define a new theory of discrete Riemann surfaces and present its basic results. The key idea is to consider not only a cellular decomposition of a surface, but the union with its dual. Discrete holomorphy is defined by a straightforward…

We discuss the utility of analytical and numerical investigation of spin models, in particular spin glasses, on ordinary ``thin'' random graphs (in effect Feynman diagrams) using methods borrowed from the ``fat'' graphs of two dimensional…

This is the first in a series of articles about recovering the full algebraic structure of a boundary conformal field theory (CFT) from the scaling limit of the critical Ising model in slit-strip geometry. Here, we introduce spaces of…

We consider a compact Riemann surface $\mathscr{R}$ with a complex of non-intersecting Jordan curves, whose complement is a pair of Riemann surfaces with boundary, each of which may be possibly disconnected. We investigate conformally…

Sections of line bundles on 2 dimensional surfaces in 3 dimensional space can have many distinct shapes. For practical purposes we prefer smooth sections that are visibly easy to follow. This is why smoothing operators have been developed…

Plane-based Geometric Algebra (PGA) has revealed points in a $d$-dimensional pseudo-Euclidean space $\mathbb{R}_{p,q,1}$ to be represented by $d$-blades rather than vectors. This discovery allows points to be factored into $d$ orthogonal…

We establish the relation of the spin tomogram to the Wigner function on a discrete phase space of qubits. We use the quantizers and dequantizers of the spin tomographic star-product scheme for qubits to derive the expression for the kernel…

We study the solutions of the T-system for type A, also known as the octahedron equation, viewed as a 2+1-dimensional discrete evolution equation. These may be expressed entirely in terms of the stepped surface over which the initial data…

Let $G$ be a compact connected Lie group, and $M$ a compact Hamiltonian $G$-space, with moment map $J$. For each $G$-equivariant Hermitian vector bundle $E$ over $M$, one has an associated twisted Spin-C Dirac operator, whose equivariant…

We present an algorithmic approach to the problem of existence of spin structures on flat manifolds. We apply our method in the cases of flat manifolds of dimensions 5 and 6.

We develop the partitioning technique for quantum discrete systems. The graph consists of several subgraphs: a central graph and several branch graphs, with each branch graph being rooted by an individual node on the central one. We show…

There are many approaches to the classification of Morse functions and their gradient fields (Morse Fields) on 2-surfaces. This paper studies the gluings of quadrilaterals and the classification of topological surfaces obtained by gluing…

A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete…

We construct algebras of pseudodifferential operators on a continuous family groupoid G that are closed under holomorphic functional calculus, contain the algebra of all pseudodifferential operators of order 0 on G as a dense subalgebra,…

We introduce a spin field approach, that is compatible with the Cartan moving frame method, to describe the submanifold in a flat space. In fact, we consider a kind of spin field $\psi$, that satisfies a Killing spin field equation…

We propose a basic theory of nonrelativistic spinful electrons on curves and surfaces. In particular, we discuss the presence and effects of spin connections, which describe how spinors and vectors couple to the geometry of curves and…

The problem of enumerating dimers on an M x N net embedded on non-orientable surfaces is considered. We solve both the Moebius strip and Klein bottle problems for all M and N with the aid of imaginary dimer weights. The use of imaginary…

We develop general techniques for computing the fundamental group of the configuration space of $n$ identical particles, possessing a generic internal structure, moving on a manifold $M$. This group generalizes the $n$-string braid group of…