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This paper relates skein spaces based on the Kauffman bracket and spin structures. A spin structure on an oriented 3-manifold provides an isomorphism between the skein space for parameter A and the skein space for parameter -A. There is an…

General Relativity and Quantum Cosmology · Physics 2009-10-28 John W. Barrett

We observe that fullerene graphs are one-skeletons of polyhedra, which can be realized with all dihedral angles equal to $\pi/2$ in a hyperbolic 3-dimensional space. One of the most important invariants of such a polyhedron is its volume.…

Geometric Topology · Mathematics 2020-11-06 Andrey Egorov , Andrei Vesnin

We investigate the holonomy group of a linear metric connection with skew-symmetric torsion. In case of the euclidian space and a constant torsion form this group is always semisimple. It does not preserve any non-degenerated 2-form or any…

Differential Geometry · Mathematics 2013-11-06 Ilka Agricola , Thomas Friedrich

We show that given a conformal structure whose holonomy representation fixes a totally lightlike subspace of arbitrary dimension, there is always a local metric in the conformal class off a singular set which is Ricci-isotropic and gives…

Differential Geometry · Mathematics 2014-08-12 Andree Lischewski

We present a comprehensive construction of scalar, vector and tensor harmonics on maximally symmetric three-dimensional spaces. Our formalism relies on the introduction of spin-weighted spherical harmonics and a generalized helicity basis…

General Relativity and Quantum Cosmology · Physics 2019-12-25 Cyril Pitrou , Thiago S. Pereira

Penrose's spinor calculus of 4-dimensional Lorentzian geometry is extended to the case of 5-dimensional Lorentzian geometry. Such fruitful ideas in Penrose's spinor calculus as the spin covariant derivative, the curvature spinors or the…

General Relativity and Quantum Cosmology · Physics 2010-01-15 Alfonso García-Parrado Gómez-Lobo , José M. Martín-García

We are studying the harmonic and twistor equation on Lorentzian surfaces, that is a two dimensional orientable manifold with a metric of signature $(1,1)$. We will investigate the properties of the solutions of these equations and try to…

Differential Geometry · Mathematics 2010-12-30 Frederik Witt

We develop an Hamiltonian representation of the sl(2,C) algebra on a phase space consisting of N copies of twistors, or bi-spinors. We identify a complete set of global invariants, and show that they generate a closed algebra including…

General Relativity and Quantum Cosmology · Physics 2015-05-28 Maité Dupuis , Laurent Freidel , Etera R. Livine , Simone Speziale

The $sp(2M)$ invariant unfolded system is considered in the periodic twistor-like spinor space. Complete set of non-trivial charges corresponding to the global symmetry compatible with the periodicity conditions is constructed. Residual…

High Energy Physics - Theory · Physics 2017-06-28 Y. O. Goncharov , M. A. Vasiliev

We show that the space of gravitational spinors in eleven dimensions, defined by equations $\Gamma_{\alpha\beta}^i\lambda^{\alpha}\lambda^{\beta}=0$ admits a desingularization with nice geometric properties. In particular the…

High Energy Physics - Theory · Physics 2011-08-29 M. V. Movshev

We develop the theory of spinorial polyforms associated with bundles of irreducible Clifford modules of non-simple real type, obtaining a precise characterization of the square of an irreducible real spinor in signature $(p-q) =…

Differential Geometry · Mathematics 2024-05-08 C. S. Shahbazi

Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It…

Mathematical Physics · Physics 2015-12-07 V. V. Varlamov

We show how the space spinor formalism for 2-component spinors can be used to construct estimates for spinor fields satisfying first order equations. We discuss the connection of the approach presented in this article with other strategies…

General Relativity and Quantum Cosmology · Physics 2025-12-25 Mariem Magdy , Juan A. Valiente Kroon

We present a Lagrangian formulation for 4d integer-spin relativistic fields in the 5d space spanned by two conjugate Weyl spinors and a Lorentz-invariant proper-time coordinate. We construct a manifestly Poincare-invariant free classical…

High Energy Physics - Theory · Physics 2023-01-06 N. G. Misuna

The spinor-helicity formalism in particle physics gives rise to natural subvarieties in the product of two Grassmannians. These include two-step flag varieties for subspaces of complementary dimension. Taking Hadamard products leads to…

Algebraic Geometry · Mathematics 2025-08-27 Yassine El Maazouz , Anaëlle Pfister , Bernd Sturmfels

Using the characterization of the spin representation in terms of exterior forms, we give a complete classification of invariant spinors on the nine homogeneous realizations of the sphere $S^n$. In each of the cases we determine the…

Differential Geometry · Mathematics 2023-05-10 Ilka Agricola , Jordan Hofmann , Marie-Amélie Lawn

The concepts of compact and projectively-compact spin-local spinor vertices are introduced. Vertices of this type are shown to be space-time spin-local, i.e. their restriction to any finite subset of fields is space-time local. The known…

High Energy Physics - Theory · Physics 2022-09-08 M. A. Vasiliev

In this review, basic definitions of spin geometry are given and some of its applications to supersymmetry, supergravity and condensed matter physics are summarized. Clifford algebras and spinors are defined and the first-order differential…

Mathematical Physics · Physics 2018-01-30 Ümit Ertem

We construct Schroedinger-like solutions of the Vasiliev higher spin theory in D>3 dimension. Symmetries of such solutions and the linearised equation of motion for the scalar on such backgrounds are analysed. We further propose Galilean…

High Energy Physics - Theory · Physics 2016-06-15 Yang Lei , Cheng Peng

In this paper we give a thoughtful exposition of the hyperbolic Clifford algebra of multivecfors which is naturally associated with a hyperbolic space, whose elements are called vecfors. Geometrical interpretation of vecfors and…

Mathematical Physics · Physics 2007-05-23 W. A. Rodrigues , Q. A. G. de Souza