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Results tagged with spin-geometry
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user 21564
For questions about spin manifolds, the groups $\operatorname{Spin}(n)$, as well as generalisations such as $\operatorname{Pin}^{\pm}(n)$ and $\operatorname{Spin}^c(n)$. This tag should also be used for any questions about the geometry of spin manifolds, including questions involving Dirac operators and the Lichnerowicz formula.
17
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2
answers
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An orientable non-spin${}^c$ manifold with a spin${}^c$ covering space
Is there a closed, smooth, orientable manifold which is not spin${}^c$ but has a finite cover which is spin${}^c$?
Such examples exist when spin${}^c$ is replaced by spin: an Enriques surface is …
- 19.3k
23
votes
2
answers
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If the universal cover of a manifold is spin, must it admit a finite cover which is spin?
If $M$ is non-orientable, then it has a finite cover which is orientable (in particular, the orientable double cover).
If $M$ is non-spin, then it does not necessarily have a finite cover which is spi …
- 19.3k