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Results tagged with spin-geometry
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user 3460
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.
2
votes
Different definitions of spin structures
As Liviu says, these properties follow from the usual definition of spin structures (in dimension 4). It's a little more work to prove that the existence of these bundles with Clifford multiplication …
- 19.4k
3
votes
Topology of the Universal Spinor Field Bundle
I think that much of what you want to know can be summarized in the question: how do you compare spin bundles for different metrics. This question, at least in the Riemannian setting, is treated with …
- 19.4k
12
votes
Harmonic spinors on closed hyperbolic manifolds
I'm happy to be able to answer my own question! John Ratcliffe, Steven Tschantz and I showed that the Dirac operator on the Davis manifold (a closed hyperbolic 4-manifold constructed by Mike Davis) ha …
- 19.4k
7
votes
Converse to Lichnerowicz Vanishing Theorem?
This is far from true! For a generic metric on a spin manifold of dimension at least 3, the kernel of the Dirac operator will be as small as it can be, subject to the index theorem. This was proved by …
- 19.4k