Related papers: Skein spaces and spin structures
We examine basis functions on momentum space for the three dimensional Euclidean Snyder algebra. We argue that the momentum space is isomorphic to the SO(3) group manifold, and that the basis functions span either one of two Hilbert spaces.…
A version of Kirby calculus for spin and framed three-manifolds is given and is used to construct invariants of spin and framed three-manifolds in two situations. The first is ribbon *-categories which possess odd degenerate objects. This…
A 3-dimensional Riemannian manifold equipped with a tensor structure of type $(1,1)$, whose third power is the identity, is considered. This structure and the metric have circulant matrices with respect to some basis, i.e., these structures…
We systematically discuss connections on the spinor bundle of Cahen-Wallach symmetric spaces. A large class of these connections is closely connected to a quadratic relation on Clifford algebras. This relation in turn is associated to the…
The article is dedicated to q-deformed versions of spinor calculus. As a kind of review, the most relevant properties of the two-dimensional quantum plane are summarized. Additionally, the relationship between the quantum plane and…
Spinor structure is understood as a totality of tensor products of biquaternion algebras, and the each tensor product is associated with an irreducible representation of the Lorentz group. A so-defined algebraic structure allows one to…
We generalize the spinorial characterization of isometric immersions of surfaces in R^3 given by T. Friedrich (On the spinor representation of surfaces in Euclidean 3-space, J. Geom. Phys. 28 (1998)) to surfaces in S^3 and H^3. The main…
The Kauffman bracket skein modules, S(M,A), have been calculated for A=+1,-1, for all 3-manifolds M by relating them to the SL(2,C)-character varieties. We extend this description to the case when A is a 4-th root of 1 and M is either a…
Non-orientable nanostructures are becoming feasable today. This lead us to the study of spin in these geometries. Hence a physically sound definition of spin is suggested. Using our definition, we study the question of the number of…
We introduce various versions of spin structures on free loop spaces of smooth manifolds, based on a classical notion due to Killingback, and additionally coupled to two relations between loops: thin homotopies and loop fusion. The central…
Local SU(3)-structures on an oriented submanifold of Spin(7)-manifold are determined and their types are characterized in terms of the shape operator and the type of the Spin(7)-structure. An application to Bryant \cite{MR89b:53084} and…
Smooth deformations of a Minkowski type metric in a four-dimensional space-time manifold are considered. Deformations of the basic spin-tensorial fields associated with this metric are calculated and their application to calculating the…
The twined almost commutative structure of the standard spectral triple on the noncommutative torus with rational parameter is exhibited, by showing isomorphisms with a spectral triple on the algebra of sections of certain bundle of…
This article explores the geometric algebra of Minkowski spacetime, and its relationship to the geometric algebra of Euclidean 4-space. Both of these geometric algebras are algebraically isomorphic to the 2x2 matrix algebra over Hamilton's…
Let M be an oriented compact 3-manifold and let T be a (loose) triangulation of M, with ideal vertices at the components of the boundary of M and possibly internal vertices. We show that any spin structure s on M can be encoded by extra…
Modular categories are a well-known source of quantum 3-manifold invariants. In this paper we study structures on modular categories which allow to define refinements of quantum 3-manifold invariants involving cohomology classes or…
In the work some relations between three techniques, Hopf's bundle, Kustaanheimo-Stiefel's bundle, 3-space with spinor structure have been examined. The spinor space is viewed as a real space that is minimally (twice as much) extended in…
We present a uniform description of $\mathrm{SU}(3)$-structures in dimension $6$ as well as $G_2$-structures in dimension $7$ in terms of a characterising spinor and the spinorial field equations it satisfies. We apply the results to…
The Kauffman bracket skein module $S(M)$ of a 3-manifold $M$ is a $\mathbb{Q}(A)$-vector space spanned by links in $M$ modulo the so-called Kauffman relations. In this article, for any closed oriented surface $\Sigma$ we provide an explicit…
We classify spin structures on the noncommutative torus, and find that the noncommutative n-torus has 2^n spin structures, corresponding to isospectral deformations of spin structures on the commutative n-torus. For n>3 the classification…