arXiv research

Study ${ m Spin}(7)$-dDT connections on manifolds with ${ m Spin}(7)$-structures.

First non-trivial examples of deformed Spin(7)-instantons constructed.

The paper studies curvature identities and solitons on Spin(7)-manifolds.

New $Spin(7)$-instantons constructed on Joyce's manifold.

We study compact, simply connected, homogeneous 8-manifolds admitting invariant Spin(7)-structures, classifying all canonical presentations G/H of such spaces, with G simply connected. For each presentation, we exhibit explicit examples of invariant Spin(7)-structures and we describe their type, according to Fernández …

Covariant formulation of Barbero-Immirzi connections for spin manifolds.

Study on instantons in $G_2$ and $Spin(7)$ manifolds.

Extended spinor connections associated with composite spin-tensorial bundles are considered. Commutation relationships for covariant and multivariate differentiations and corresponding curvature spin-tensors are derived.

Study proves a conjecture for certain spin manifolds.

Let J be the exceptional Jordan algebra over R and J^C its complexification. Then the simply connected compact exceptional Lie group F_4 acts on J and F_4 has three orbit types which are F_4/F_4, F_4/Spin(9), F_4/Spin(8). Similarly the simply connected compact exceptional Lie group E_6 acts on J^C and E_6 has five orbi…

Researchers compute mod 2 Seiberg-Witten invariants for spin structures and families.

Study classifies moduli spaces of spin connections on 3D homogeneous spaces.

Abstract: Review and definitions of generalised spin structures, their connections, and symmetry algebra.

Proves Rudyak's conjecture for low-dimensional simply connected spin manifolds.

Cobordism and signatures of manifolds with similar fundamental groups.

We study Spin(9)-structures on 16-dimensional Riemannian manifolds and characterize the geometric types admitting a connection with totally skew-symmetric torsion.

The second Betti number of a smooth, closed, connected and simply connected, four-dimensional spin manifold is greater or equal 11/8 times the abolute value of its signature.

Study Spin(7) instantons and HYM connections on Stenzel metric.

Alternative definition of dDT connections for Spin(7) manifolds.

M-theory on compact eight-manifolds with $\mathrm{Spin}(7)$-holonomy is a framework for geometric engineering of 3d $\mathcal{N}=1$ gauge theories coupled to gravity. We propose a new construction of such $\mathrm{Spin}(7)$-manifolds, based on a generalized connected sum, where the building blocks are a Calabi-Yau four…

We explore differential and algebraic operations on the exterior product of spinor representations and their twists that give rise to cohomology, the spin cohomology. A linear differential operator $d$ is introduced which is associated to a connection $\nabla$ and a parallel spinor $ζ$, $\nablaζ=0$, and the algebraic o…

Joyce constructed examples of compact eight-manifolds with holonomy Spin(7), starting with a Calabi-Yau four-orbifold with isolated singular points of a special kind. That construction can be seen as the gluing of ALE Spin(7)-manifolds to each singular point of the Calabi-Yau four-orbifold divided by an anti-holomorphi…

We study spin structures on compact simply-connected homogeneous pseudo-Riemannian manifolds (M = G/H, g) of a compact semisimple Lie group G. We classify flag manifolds F = G/H of a compact simple Lie group which are spin. This yields also the classification of all flag manifolds carrying an invariant metaplectic stru…

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 result of this article is an equivalence between these enhanced versions of spin…

Formula derived for Spin(7)-structures on 8D manifolds.

The higher spin Laplace operator has been constructed recently as the generalization of the Laplacian in higher spin theory. This acts on functions taking values in arbitrary irreducible representations of the Spin group. In this paper, we first provide a decomposition of the higher spin Laplace operator in terms of Rr…

Article finds a geometric connection between structures on manifolds.

According to the work of Kontsevich-Zorich, the invariant that classifies non-hyperelliptic connected components of the moduli spaces of Abelian differentials with prescribed singularities,is the parity of the spin structure. We show that for the moduli space of quadratic differentials, the spin structure is constant o…

Defines a volume functional for Hermitian connections on manifolds, proving its properties and connections.

We define spin frames, with the aim of extending spin structures from the category of (pseudo-)Riemannian manifolds to the category of spin manifolds with a fixed signature on them, though with no selected metric structure. Because of this softer requirements, transformations allowed by spin frames are more general tha…

Classifies invariant spin structures on spheres.

We present a classification theorem for closed smooth spin 2-connected 7-manifolds M. This builds on the almost-smooth classification from the first author's thesis. The main additional ingredient is an extension of the Eells-Kuiper invariant for any closed spin 7-manifold, regardless of whether the spin characteristic…

In this paper we introduce the Dirac and spin-Dirac operators associated to a connection on Riemann-Cartan space(time) and standard Dirac and spin-Dirac operators associated with a Levi-Civita connection on a Riemannian (Lorentzian) space(time) and calculate the square of these operators, which play an important role i…

Spin Lefschetz fibrations can represent any group and lattice point.

Study spin chains and sigma models on flag manifolds, calculating spectra and geodesics.

The paper proves a spin manifold's 4D quasi-Einstein satisfies Hitchin-Thorpe inequality.

We study the connected components of the space of higher spin bundles on hyperbolic Klein surfaces. A Klein surface is a generalisation of a Riemann surface to the case of non-orientable surfaces or surfaces with boundary. The category of Klein surfaces is isomorphic to the category of real algebraic curves. An m-spin …

We define spin-c prequantization of a symplectic manifold to be a spin-c structure and a connection which are compatible with the symplectic form. We describe the cutting of an S^1-equivariant spin-c prequantization. The cutting process involves a choice of a spin-c prequantization for the complex plane. We prove that …

Geometrically constructs dilogarithm from Chern-Simons theory.

Classifies Spin(7) structures on compact 8-manifolds with abelian fundamental group.

We show how a suitably twisted Spin-cobordism spectrum connects to the question of existence of metrics of positive scalar curvature on closed, smooth manifolds by building on fundamental work of Gromov, Lawson, Rosenberg, Stolz and others. We then investigate this parametrised spectrum, compute its $mod~2$-cohomology …

New criterion for Ricci-flat manifolds with non-vanishing Rosenberg index.

Study uncoupled solutions to Dirac-Yang-Mills equations on spin manifolds.

New method classifies spin 4-manifolds using Kervaire-Milnor invariant.

Researchers classify and construct various instantons and connections on a specific 8-manifold.

New spinor fields reveal local or global geometric properties of manifolds.

We show that on every Spin(7) manifold there always exists a unique linear connection with totally skew-symmetric torsion preserving a nontrivial spinor and the Spin(7) structure. We express its torsion and the Riemannian scalar curvature in terms of the fundamental 4-form. We present an explicit formula for the Rieman…

A treatment of the spin-statistics relation in nonrelativistic quantum mechanics due to Berry and Robbins [Proc. R. Soc. Lond. A (1997) 453, 1771-1790] is generalised within a group-theoretical framework. The construction of Berry and Robbins is re-formulated in terms of certain locally flat vector bundles over n-parti…