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Results tagged with spin-geometry
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user 6999
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.
14
votes
Accepted
Commutative spectral triples
From the perspective of the Gelfand–Naimark theorem, the heart of the reconstruction theorem is the following statement, Theorem 11.4 in Connes's paper:
Let $\mathcal{A}$ be a commutative unital c …
- 2,385
4
votes
Spinor bundle tensored with certain line bundle gives the dual spinor bundle
Let $c : \mathbb{C}\mathrm{l}_n \to \operatorname{End}(S_n)$ be your irrep, so that the “dual” irrep $c^\ast : \mathbb{C}\mathrm{l}_n \to \operatorname{End}(S_n^\ast)$ is defined by
$$
\forall x \in …
- 2,385
10
votes
what is a spinor structure?
Just to elaborate a bit in explicitly differential-geometric terms on MTS's answer, which refers to certain results of Plymen's originally restated in terms of Morita equivalence (via the dictionary g …
- 2,385
18
votes
Accepted
Noncommutative smooth manifolds
I'm a bit wary of resurrecting such an old question, but given that the precise content of the reconstruction theorem doesn't seem to be terribly well disseminated, please permit me to cross-post from …
- 2,385