Revisiting pinors and orientability
type: Item
instance of: scholarly article
zbMATH Open document ID: 1261.57022
author: Fabio Ferrari Ruffino
author: Raffaele Savelli
author: L. Bonora
publication date: 2012-09-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/0907.4334
Mathematics Subject Classification ID: 57R15
Mathematics Subject Classification ID: 53C10
zbMATH DE Number: 6079013
zbMATH Keywords: double coverings
zbMATH Keywords: discrete group of transformations
zbMATH Keywords: pin structures
zbMATH Keywords: pinors
MaRDI profile type: Publication
arXiv ID: 0907.4334
arXiv classification: math-ph
arXiv classification: hep-th
arXiv classification: math.MP
title: Revisiting pinors and orientability
published in: Bollettino dell'Unione Matematica Italiana. Series IX
review text: Let \(\widetilde X\) be the orientable double cover of a non-orientable manifold \(X\) equipped with the orientation-reversing involution \(\tau\) such that \(\widetilde X/\tau\simeq X\). The authors study the relations between pin structures on \(X\) and \(\tau\)-invariant pin structures on \(\widetilde X\). They show that there is not a simple bijection, but that the natural map induced by pull-back is neither injective nor surjective. By imposing additional conditions the authors recover the full correspondence. Moreover, the authors consider examples of surfaces, with detailed computations for the real projective plane, the Klein bottle and the Moebius strip.
reviewed by: Andrew Bucki
description: scientific article; zbMATH DE number 6079013