Related papers: Classification of spin structures on the noncommut…

Main topic of the paper is the determination, for a compact complex manifold $M$, of the class of manifolds $X$ which are deformation equivalent to it. If $M$ is a complex torus, then also $X$ is so. After describing the structure of…

We show that in certain superstring compactifications, gauge theories on noncommutative tori will naturally appear as D-brane world-volume theories. This gives strong evidence that they are well-defined quantum theories. It also gives a…

The configuration space C^n of unordered n-tuples of distinct points on a torus T^2 is a non-singular complex algebraic variety. We study holomorphic self-maps of C^n and prove that for n>4 any such map F either carries the whole of C^n…

Motivated by localization theorems on moduli spaces, we prove a structural classification of Deligne-Mumford stacks with an action of a torus where the induced action on the coarse moduli space is trivial. We also establish a general local…

A twist is a datum playing a role of a local system for topological $K$-theory. In equivariant setting, twists are classified into four types according to how they are realized geometrically. This paper lists the possible types of twists…

We study three-dimensional path geometries with nontrivial torsion of maximal rank. We introduce the notion of constant torsion and show that such path geometries are in one-to-one correspondence with certain cone structures modeled on…

The multiplicities of the decomposition of the product of an arbitrary number $n$ of spin $s$ states into irreducible $SU(2)$ representations are computed. Two complementary methods are presented, one based on random walks in representation…

It is known that the complex projective space $\mathbb{CP}^n$ admits a spin structure if and only if $n$ is odd. In this paper, we provide another proof that $\mathbb{CP}^{2m}$ does not admit a spin structure, by using a circle action.

Non-Hermitian systems have been discussed mostly in the context of open systems and nonequilibrium. Recent experimental progress is much from optical, cold-atomic, and classical platforms due to the vast tunability and clear identification…

For the flip action of $\mathbb{Z}_2$ on an $n$-dimensional noncommutative torus $A_\theta,$ using an exact sequence by Natsume, we compute the K-theory groups of $A_\theta \rtimes \mathbb{Z}_2$. The novelty of our method is that it also…

In two former papers, the authors independently proved that the space of hyperbolic cone-3-manifolds with cone angles less than 2{\pi} and fixed singular locus is locally parametrized by the cone angles. In this sequel, we investigate the…

In this paper we study the moduli space of standard holomorphic structures on a noncommutative complex two torus. It will be shown that the moduli space is naturally identified with the moduli space of stable bundles on an elliptic curve.…

We completely determine the mod $2$ Seiberg-Witten invariants for any spin structure on any closed, oriented, smooth $4$-manifold $X$. Our computation confirms the validity of the simple type conjecture mod $2$ for spin structures. Our…

We construct three dimensional N=1 Chern-Simons theories living on M2 branes probing Spin(7) cones. We consider Spin(7) manifolds obtained as quotients of Calabi-Yau four-folds by an anti-holomorphic involution, following a construction by…

The study of higher tangential structures, arising from higher connected covers of Lie groups (String, Fivebrane, Ninebrane structures), require considerable machinery for a full description, especially for connections to geometry and…

For $g \ge 5$, we give a complete classification of the connected components of strata of abelian differentials over Teichm\"uller space, establishing an analogue of Kontsevich and Zorich's classification of their components over moduli…

We classify toroidal solenoids defined by non-singular $n\times n$-matrices $A$ with integer coefficients by studying associated first \^Cech cohomology groups. In a previous work, we classified the groups in the case $n=2$ using…

We describe noncommutative geometric aspects of twisted deformations, in particular of the spheres in Connes and Landi [8] and in Connes and Dubois Violette [7], by using the differential and integral calculus on these spaces that is…

If a closed 3-manifold M supports a closed, nonsingular, irrational 1-form which linearly deforms into contact forms, then M supports a K-contact form. On the 3-torus, a closed nonsingular 1-form deforms linearly into contact forms if and…

In the framework of noncommutative geometry we describe spinor fields with nonvanishing winding number on a truncated (fuzzy) sphere. The corresponding field theory actions conserve all basic symmetries of the standard commutative version…