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

Brunella's classification implies that every smooth foliation on a compact complex surface admits a singular transversely projective structure. However, Biswas and Dumitrescu's recent work shows that certain foliations on compact complex…

The explicit expressions describing the structure function g_1 at arbitrary x and Q^2 are obtained. In the first place, they combine the well-known DGLAP expressions for g_1 with the total resummation of leading logarithms of x, which makes…

The engineered spin structures recently built and measured in scanning tunneling microscope experiments are calculated using density functional theory. By determining the precise local structure around the surface impurities, we find the Mn…

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…

In this paper we construct non-simply connected contact manifolds $M$ of dimension $\geq5$ such that $M\times S^1$ does not admit a symplectic structure.

We find and classify possible equivariant spin structures with Dirac operators on the noncommutative torus, proving that similarly as in the classical case the spectrum of the Dirac operator depends on the spin structure.

In two-dimensional Euclidean plane, existence of second-order integrals of motion is investigated for integrable Hamiltonian systems involving spin (\emph{e.g.,} those systems describing interaction between two particles with spin 0 and…

Let $(M,g)$ be a pseudo-Riemannian manifold of signature $(p,q)$. We compute the obstruction for a vector bundle $S$ over $(M,g)$ to admit a Dirac operator whose principal symbol induces on $S$ the structure of a bundle of irreducible real…

We prove that a closed manifold which admits a symplectic-Lipschitz structure has non-vanishing even-degree cohomology groups with real coefficients. In particular, spheres $S^{2n}, n \geq 2$ do not admit symplectic-Lipschitz structures.

We present an alternative formalism for modeling spin. The ontological elements of this formalism are base-2 sequences of length $n$. The machinery necessary to model physics is then developed by considering correlations between base-2…

The talk presents an ab initio construct of the spacetime structure underlying massive gravitinos. We argue that single spin interpretation of massive gravitino is untenable, and that a spin measurement in the rest frame for an unpolarized…

It is well known that spinors on oriented Riemannian manifolds cannot be defined as sections of a vector bundle associated with the frame bundle. For this reason spin and spin^c structures are often introduced. In this paper we prove that…

We study three distinct types of planar, spherically symmetric and localized structures, one of them having non-topological behavior and the two others being of topological nature. The non-topological structures have energy density…

In this paper, it is shown that non-isomorphic effective linear circle actions yield non-diffeomorphic differential structures on the corresponding orbit spaces.

We show that the connected sum of two copies of real projective 3-space does not admit a real projective structure. This is the first known example of a connected 3-manifold without a real projective structure.

Let $M^m$ be a compact oriented smooth manifold which admits a smooth circle action with isolated fixed points which are isolated as singularities as well. Then all the Pontryagin numbers of $M^m$ are zero and its Euler number is…

We show that all vector bundles over CP^2 which are not spin admit a complete metric with nonnegative sectional curvature. In the proof we construct a nonnegatively curved metric on the corresponding principle bundle by showing that it…

This paper investigates some actions "\`a la Johnson" on the set, denoted by ${\cal E}$, of Spin-structures which are interpreted as special double-coverings of a trivial $S^1-$fibration over a non-orientable surface $N_{g+1}$. The group…

The discrete symmetries of the Lorentz group are on the one hand a `complex' interplay between linear and anti-linear operations on spinor fields and on the other hand simple linear reflections of the Minkowski space. We define operations…

This paper proves that there are no compact forms for a large class of homogeneous spaces admitting actions by higher-rank semisimple Lie groups. It builds on Zimmer's approach for studying such spaces using cocycle superrigidity. The proof…