Related papers: Spin Structures on Generalized Real Bott Manifolds

The main aim of this article is to give a necessary and sufficient condition for a real Bott manifold to admit a spin structure and further give a combinatorial characterization for the spin structure in terms of the associated acyclic…

We give a necessary and sufficient condition for existence of spinc structures on real Bott manifolds.

Let $$M_{n}\stackrel{\mathbb R P^1}\to M_{n-1}\stackrel{\mathbb R P^1}\to\ldots\stackrel{\mathbb R P^1}\to M_{1}\stackrel{\mathbb R P^1}\to M_0 = \{ \bullet\} $$ be a sequence of real projective bundles such that $M_i\to M_{i-1}$,…

Let $M$ be a real Bott manifold with K\"{a}hler structure. Using Ishida characterization \cite{I11} we give necessary and sufficient condition for the existence of the spin-structure on $M$. In proof we use the technic developed in…

Let M be a real Bott manifold with K\"{a}hler structure. Using Ishida characterization we give necessary and sufficient condition for the existence of the Spin-structure on M. In proof we use the technic developed in Popko, Szczepa\'{n}ski…

We give a necessary and suffcient condition for almost-flat manifolds with cyclic holonomy to admit a Spin structure. Using this condition we find all 4-dimensional orientable almost- flat manifolds with cyclic holonomy that do not admit a…

Generalised spin structures, or r-spin structures, on a 2-dimensional orbifold \Sigma are r-fold fibrewise connected coverings (also called r-th roots) of its unit tangent bundle ST\Sigma. We investigate such structures on hyperbolic…

Generalized Bott manifolds (over $\mathbb C$ and $\mathbb R$) have been defined by Choi, Masuda and Suh. In this article we extend the results of arXiv:1609.05630 on the topology of real Bott manifolds to generalized real Bott manifolds. We…

Spinorial methods have proven to be a powerful tool to study geometric properties of spin manifolds. Our aim is to continue the spinorial study of manifolds that are not necessarily spin. We introduce and study the notion of $G$-invariance…

Every Dirac spin structure on a world manifold is associated with a certain gravitational field, and is not preserved under general covariant transformations. We construct a composite spinor bundle such that any Dirac spin structure is its…

Masuda (2008) provided the characterization of real Bott manifolds in terms of three operations on upper triangular matrices. We provide a combinatorial characterization of real Bott manifolds up to diffeomorphism in terms of operations on…

It was recently pointed out by E. Witten that for a D-brane to consistently wrap a submanifold of some manifold, the normal bundle must admit a Spin^c structure. We examine this constraint in the case of type II string compactifications…

We completely characterize real Bott manifolds up to affine diffeomorphism in terms of three simple matrix operations on square binary matrices obtained from strictly upper triangular matrices by permuting rows and columns simultaneously.…

Classically, a spin structure on the loop space of a manifold is a lift of the structure group of the looped frame bundle from the loop group to its universal central extension. Heuristically, the loop space of a manifold is spin if and…

For each integer $d$ at least two, we construct non-spin closed oriented flat manifolds with holonomy group $\mathbb Z_2^d$ and with the property that all of their finite proper covers have a spin structure. Moreover, all such covers have…

We give necessary and sufficient conditions for the existence of pin+, pin- and spin structures on Riemannian manifolds with holonomy group $Z_2^k$. For any n>3 (resp. n>5) we give examples of pairs of compact manifolds (resp. compact…

We present an algorithmic approach to the problem of existence of spin structures on flat manifolds. We apply our method in the cases of flat manifolds of dimensions 5 and 6.

A real Bott manifold is the total space of an iterated $\RP ^1$-bundles over a point, where each $\RP^1$-bundle is the projectivization of a Whitney sum of two real line bundles. In this paper, we characterize real Bott manifolds which…

Let $M$ be an oriented closed 4-manifold and $\cL$ be a $spin^c$ structure on $M$. In this paper we prove that under a suitable condition the Seiberg-Witten moduli space has a canonical spin structure and its spin bordism class is an…

Almost-flat manifolds were defined by Gromov as a natural generalisation of flat manifolds and as such share many of their properties. Similarly to flat manifolds, it turns out that the existence of a spin structure on an almost-flat…