Related papers: On Dijkgraaf-Witten Type Invariants

A piecewise flat manifold is a triangulated manifold given a geometry by specifying edge lengths (lengths of 1-simplices) and specifying that all simplices are Euclidean. We consider the variation of angles of piecewise flat manifolds as…

Let X be a smooth complex variety and Y be a closed subvariety of X, or more generally, a closed subscheme of X. We are interested in invariants attached to the singularities of the pair (X, Y). We discuss various methods to construct such…

We introduce a geometric construction of a gauge field theory of a complex adaptive system. It is based on a suitable simplicial formulation of a discrete geometry that manifests relevant properties valid in the classical differentiable…

Using the S--matrix pinch technique we obtain to one loop order, gauge independent $\gamma W^-W^+$ and $Z W^-W^+$ vertices in the context of the standard model, with all incoming momenta off--shell. We show that the vertices so constructed…

A classification of the possible symmetric principal bundles with a compact gauge group, a compact symmetry group and a base manifold which is regularly foliated by the orbits of the symmetry group is derived. A generalization of Wang's…

Let $f$ be the gluing map of a Heegaard splitting of a 3-manifold $W$. The goal of this paper is to determine the information about $W$ contained in the image of $f$ under the symplectic representation of the mapping class group. We prove…

This paper is the first in a series of three devoted to the smooth classification of simply connected elliptic surfaces. The method is to compute some coefficients of Donaldson polynomials of $SO(3)$ invariants whose second Stiefel-Whitney…

Given a compact K\"ahler manifold, Geometric Invariant Theory is applied to construct analytic GIT-quotients that are local models for a classifying space of (poly)stable holomorphic vector bundles containing the coarse moduli space of…

Given a finite connected graph $\Lambda$, the space of $SU(2)$ lattice gauge-fields on $\Lambda$, modulo gauge transformations, is a Lagrangian submanifold -- with mild singularities -- of the $SU(2)$ character variety (= phase-space of…

Given a group G, we use involutary Hopf G-coalgebras to define a scalar invariant of flat G-bundles over 3-manifolds. When G=1, this invariant equals to the one of 3-manifolds constructed by Kuperberg from involutary Hopf algebras. We give…

Let $E\to B$ be a smooth vector bundle of rank $n$, and let $P \in I^p(GL(n,\mathbb{R}))$ be a $GL(n,\mathbb{R})$-invariant polynomial of degree $p$ compatible with a universal integral characteristic class $ u \in…

Using the S--matrix pinch technique we obtain to one loop order gauge independent $\gamma W^-W^+$ and $Z W^-W^+$ vertices in the context of the standard model, with all incoming momenta off--shell. We show that the vertices so constructed…

We prove that every suitable $4$-manifold with $b_1=0$ and with an embedded Riemann surface of genus $2$ is of simple type. We find a relationship between the basic classes of two of these $4$-manifolds and those of the connected sum along…

We construct a dynamical lattice model based on a crossed module of possibly non-abelian finite groups. Its degrees of freedom are defined on links and plaquettes, while gauge transformations are based on vertices and links of the…

Invariants for framed links in $S^3$ obtained from Chern-Simons gauge field theory based on an arbitrary gauge group (semi-simple) have been used to construct a three-manifold invariant. This is a generalization of a similar construction…

We obtain a simple formula for the multiplicity of eigenvalues of the Hodge-Laplace operator, $\Delta_f$, acting on sections of the full exterior bundle over an arbitrary compact flat Riemannian n-manifold M with holonomy group Z_2^k, with…

We report on a study of a one-dimensional linear photonic lattice hosting, simultaneously, fundamental and dipolar modes at every site. We show how, thanks to the interaction between the different orbital modes, this minimal model exhibits…

Among an infinite number of possible folds, nature has chosen only about 1000 distinct folds to form protein structures. Theoretical studies suggest that selected folds are intrinsically more designable than others; these selected folds are…

In this paper we put forward a systematic and unifying approach to construct gauge invariant composite fields out of connections. It relies on the existence in the theory of a group valued field with a prescribed gauge transformation. As an…

Levin-Wen models are a class of two-dimensional lattice spin models with a Hamiltonian that is a sum of commuting projectors, which describe topological phases of matter related to Drinfeld centres. We generalise this construction to…