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Results tagged with spin-geometry
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user 5690
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.
9
votes
Accepted
What is the "quaternionic" super Brauer group?
The Brauer-Picard 2-category of $SuperVect_{\mathbb R}$ (let's call it $sBrPic_\mathbb R$) is the homotopy fixed points of the Brauer-Picard 2-category of $SuperVect_{\mathbb C}$ w.r.t. the involution …
- 43.2k
14
votes
Accepted
Atiyah-Bott-Shapiro Orientation
A point in the $n$th space of $MSpin$ is an $n$-dimensional manifold equipped with a spin structure. In other words, it is a manifold equipped with a bundle of bimodules between the Clifford algebra o …
- 43.2k
15
votes
What are "good" examples of spin manifolds?
If you know about Steenrod operations, here's a very convenient characterization:
A manifold $M$ is Spin iff its Poincare duality in $H^*(M,\mathbb Z/2)$ is
compatible with $Sq^1$ and $Sq^2$.
…