most recent 30 from http://mathoverflow.net 2013-05-23T16:22:25Z http://mathoverflow.net/feeds/question/107984 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/107984/low-dimensional-spin-manifolds Nastya 2012-09-24T15:08:45Z 2012-09-25T08:09:41Z

<p>I am looking for examples of 2- and 3-dimensional flat spin manifolds with Euclidean and Lorentzian signatures, which admit parallel spinors and the dimension of the space of the parallel spinors is equal to 1. At the moment I have examples only for the Lorentzian case:$\mathbb{R}^{1,1}_{*}/(Z_{2})$ (for dimension 2) and $\mathbb{R}^{1,1}_{*}/(Z_{2}) \times \mathbb{R}$ (for dimension 3). Here $\mathbb{R}^{1,1}_{*}$ means $\mathbb{R}^{1,1}\setminus {(0,0)}$ and the generator of $Z_2$ acts as $x \mapsto (-x)$. However, I am not sure if it is correct.</p>