Related papers: Spin structures on complex projective spaces and c…

We define spin structures on perfect complexes outside of characteristic two, generalizing the usual notion for vector bundles. We give an explicit local characterization of spin structures, and show that for an oriented quadratic complex…

In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel…

Let $\Sigma$ be a closed orientable surface of genus at least two, and let $X, Y$ be distinct marked Riemann surface structures on $\Sigma$, possibly with opposite orientations. In this paper, we show that there are (exactly) countably…

We study the effects of having multiple Spin structures on the partition function of the spacetime fields in M-theory. This leads to a potential anomaly which appears in the eta-invariants upon variation of the Spin structure. The main…

We show that the standard SU(n)-covariant Poisson sphere $S^{2n-1}$ is embedded in the nonstandard $SU(n+1)$-covariant Poisson complex projective spaces $CP^{n}$.

The review of the nucleon spin structure functions problems is presented. The perturbative QCD predictions for the small x behaviour of the nucleon spin structure functions are discussed. The role of the resummation of the ln^2 1/x terms is…

For certain non-magnetic solids with low symmetry the occurrence of spin-polarized longitudinal currents is predicted. These arise due to an interplay of spin-orbit interaction and the particular crystal symmetry. This result is derived…

In this article, we answer two questions of Buchanan-McKean (arXiv:2312.08209) about bordism for manifolds with spin$^h$ structures: we establish a Smith isomorphism between the reduced spin$^h$ bordism of $\mathbb{RP}^\infty$ and…

It is widely believed that Rasba spin splitting occurs only in systems lacking space inversion invariance. In this letter we present analytical analysis which suggests that non-zero Rashba spin splitting occurs in systems possessing space…

We study spin structures on Riemann and Klein surfaces in terms of divisors. In particular, we take a closer look at spin structures on hyperelliptic and $p$-gonal surfaces defined by divisors supported on their branch points. Moreover, we…

We prove that compact quaternionic-K\"ahler manifolds of positive scalar curvature admit no almost complex structure, even in the weak sense, except for the complex Grassmannians $Gr_2(C^{n+2})$. We also prove that irreducible inner…

We consider the problem of defining the structure of a smooth manifold on the various spaces of piecewise-smooth loops in a smooth finite dimensional manifold. We succeed for a particular type of piecewise-smooth loops. We also examine the…

A rational projective plane ($\mathbb{QP}^2$) is a simply connected, smooth, closed manifold $M$ such that $H^*(M;\mathbb{Q}) \cong \mathbb{Q}[\alpha]/\langle \alpha^3 \rangle$. An open problem is to classify the dimensions at which such a…

We study a two-dimensional electron system in the presence of spin-orbit interaction. It is shown analytically that the spin-orbit interaction acts as a transversal effective electric field, whose orientation depends on the sign of the…

We explicitly construct several Poisson structures with compact support. For example, we show that any Poisson structure on $\R^n$ with polynomial coefficients of degree at most two can be modified outside an open ball, such that it becomes…

We study smooth fibrations of compact torsion-free Spin(7)-manifolds by Cayley submanifolds. Using geometric and topological constraints coming from the Spin(7)-structure, we show that only two topological configurations can arise. One of…

We initiate a research program for the systematic investigation of quantum superintegrable systems involving the interaction of two non-relativistic particles with spin $1/2$ moving in the three-dimensional Euclidean space. In this paper,…

Transition metal (TM) defects in silicon carbide have favorable spin coherence properties and are suitable as quantum memory for quantum communication. To characterize TM defects as quantum spin-photon interfaces, we model defects that have…

Any nonpositively curved symmetric space admits a topological compactification, namely the Hadamard compactification. For rank one spaces, this topological compactification can be endowed with a differentiable structure such that the action…

We study conformal partial waves (CPWs) in Mellin space with totally symmetric external operators of arbitrary integer spin. The exchanged spin is arbitrary, and includes mixed symmetry and (partially)-conserved representations. In a basis…