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Results tagged with spin-geometry
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user 97265
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.
7
votes
Accepted
Spin Structure on AdS- Schwarzschild manifold
The existence or nonexistence of a spin structure on a smooth manifold $M$ is a topological question, in that it does not depend on the choice of a Riemannian metric on $M$. Spin structures are obstru …
- 6,881
10
votes
Spin-H structures
SpinH-structures were studied by Shiozaki-Shapourian-Gomi-Ryu for applications to condensed-matter physics. They prove in Lemma D.9 that a closed manifold $M$ admits a spinH-structure iff it's orienta …
- 6,881
1
vote
Accepted
Characterization of self-conjugate spin$^c$ structures
$\newcommand{\Spin}{\mathrm{Spin}}\newcommand{\Z}{\mathbb{Z}}$Here's one way to think about the data of
(self-conjugate) spin$^c$ structures. A spin$^c$ structure has the associated data of a class $c …
- 6,881
5
votes
Discrete Pin structures
Here are some partial answers.
For your first question: there are combinatorial formulas for all Stiefel-Whitney homology classes $w_k$, due to
Whitney and rediscovered by Cheeger.
Specifically, on a …
- 6,881