Related papers: 2-Categories, 4d state-sum models and gerbes
We introduce horizontal holonomy groups, which are groups defined using parallel transport only along curves tangent to a given subbundle $D$ of the tangent bundle. We provide explicit means of computing these holonomy groups by deriving…
A homology and cohomology theory for topological quandles are introduced. The relation between these (co)homology groups and quandle (co)homology groups are studied. The 1 - topological quandle cocycles are used to compute state sum…
Given a foliation, there is a well-known notion of holonomy, which can be understood as an action that differentiates to the Bott connection on the normal bundle. We present an analogous notion for Lie subalgebroids, consisting of an…
In this article, we study about the $\lambda$-statistical convergence with respect to the density of moduli and find some results related to statistical convergence as well. Also we introduce the concept of $f_\lambda$-summable sequence and…
This paper shows how to construct anomaly free world sheet actions in string theory with $D$-branes. Our method is to use Deligne cohomology and bundle gerbe theory to define geometric objects which are naturally associated to $D$-branes…
Our paper deals about identities involving Bell polynomials. Some identities on Bell polynomials derived using generating function and successive derivatives of binomial type sequences. We give some relations between Bell polynomials and…
Let $S$ be a closed oriented surface of genus $g\geq 2$. Fix an arbitrary non-elementary representation $\rho\colon\pi_1(S)\to {\rm SL}_2(\mathbb{C})$ and consider all marked (complex) projective structures on $S$ with holonomy $\rho$. We…
The purpose of this paper is to continue studying the properties of $\gamma$-regular open sets introduced and explored in [6]. The concept of $\gamma$-closed spaces have also been defined and discussed.
Given a flat connection on a manifold with values in a filtered L-infinity-algebra, we construct a morphism of coalgebras that generalizes the holonomies of flat connections with values in Lie algebras. The construction is based on…
Algebraic homology and cohomology theories for quandles have been studied extensively in recent years. With a given quandle 2(3)-cocycle one can define a state-sum invariant for knotted curves(surfaces). In this paper we introduce another…
This paper is a survey of several papers in quandle homology theory and cocycle knot invariants that have been published recently. Here we describe cocycle knot invariants that are defined in a state-sum form, quandle homology, and methods…
We develop a ready-to-use comprehensive theory for (super) 2-vector bundles over smooth manifolds. It is based on the bicategory of (super) algebras, bimodules, and intertwiners as a model for 2-vector spaces. We discuss symmetric monoidal…
In this expository article, we present a brief introduction to the theory of Hilbert modular forms and Galois representations, and describe what it means to attach a compatible system of Galois representations to a Hilbert modular form.
Holonomy groups and holonomy algebras for connections on locally free sheaves over supermanifolds are introduced. A one-to-one correspondence between parallel sections and holonomy-invariant vectors, and a one-to-one correspondence between…
The notion of holonomy $R$-matrices is introduced. It is shown how to define invariants of tangles with flat connections in a principle $G$-bundle of the complement of a tangle using holonomy $R$-matrices.
We study observables on group elements in the Ponzano-Regge model. We show that these observables have a natural interpretation in terms of Feynman diagrams on a sphere and contrast them to the well studied observables on the spin labels.…
This is the second of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern--Simons theory. We provide a definition of trace over a crossed module…
Recently twisted K-theory has received much attention due to its applications in string theory and the announced result by Freed, Hopkins and Telemann relating the twisted equivariant K-theory of a compact Lie group to its Verlinde algebra.…
The present article is the first of a series whose goal is to define a logical formalism in which it is possible to reason about genetics. In this paper, we introduce the main concepts of our language whose domain of discourse consists of a…
We construct dyonic states in 2+1-dimensional lattice Z_N-Higgs models, i.e., states which are both, electrically and magnetically charged. The associated Hilbert spaces carry charged representations of the observable algebra, the global…