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Results tagged with spin-geometry
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user 12653
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
2
answers
752
views
Twisting Spinor Bundles with Line Bundles
In a paper I am reading, the following framework was given: Let $S$ be a spinor bundle, over a Riemannian manifold $M$, with Clifford action
$$
c:S \otimes \Omega^1(M) \to S.
$$
Moreover, let $E$ be …
- 1,453
7
votes
2
answers
506
views
Spin Structures for Quaternionic-Kaehler and Hyper-Kaehler Manifolds
As is well-known (see Friedrich's book for example) every Kähler manifold is spin (or at least spin$^c$) and the Dirac is given (up to a twist) by $\partial + \partial^*$. What happens in the quaterni …
- 1,453
6
votes
1
answer
1k
views
Which Kahler Manifolds Are Spin?
As is well-known (see here for a M.O. question) all Kahler manifolds are $spin^c$. I would like to ask which are in fact $spin$.
Taking my motivation from the case of complex projective space, I mak …
- 1,453
8
votes
1
answer
306
views
K-homology classes of Dirac operators on Hermitian manifolds
Given a compact Hermitian manifold $M$, we have three canonical pseudo-differential operators on the sections of complexified de Rham complex, namely
1) (d + d$^*,\Omega^{*})$
2) ($\partial$ + $\p …
- 1,453
6
votes
1
answer
512
views
Lagrangian Grassmannian as a Spin Manifold
I am trying to better understand this nice answer to a question of mine, which states
Spin structures on a compact complex manifold $(M^{2n},J)$ are in bijective correspondence with isomorphism cl …
- 1,453