Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Spin structures and the second Stiefel-Whitney class are themselves not particularly simple, so I don't know what kind of an answer you're expecting.

2024年10月4日 · In the physics literature, it has been used the concept of Spin $^c$ structure (see for example 1) for the description of fermions in condensed matter systems (where fermions have odd U(1) charges).

2017年8月23日 · The virtue of this picture is the LES used above explains both the obstruction to and the classification(i.e., the affine structure) of spin structures. Okay, this is great, and now move on to the complex spin case.

2024年7月7日 · The map between these two things describing how the difference behaves when you complexify a spin structure is a Bockstein homomorphism $$\beta : H^1(M, \mathbb{Z}/2) \to H^2(M, \mathbb{Z})$$

2015年11月3日 · Now a typical assertion is that each spin structure induces a canonical $\mathrm{spin^c}$ structure. I tried to show that via connecting the commutative diagrams, and using the fact that there is a natural inclusion of the spin group in the $\mathrm{spin^c}$ group.

2016年9月26日 · $\begingroup$ @R_D You can think of it a few ways. Note that a double cover is the same thing as a principal O(1)-bundle, because there is an obvious map giving the action of $-1$: the map that swaps the two elements of the fiber above any given point.

Spin^c structure induced by a spin structure. 5. Spin structure and bordism. 3.

The disk has a unique spin structure, and we can ask which spin structure this induces on the boundary. Lawson/Michelson's "Spin Geometry" claims that this induces the spin structure coming from the double cover, but I'm having trouble seeing that.

2017年1月8日 · Spin structure and restriction to fibers. 2. Spinor bundles and spin structures. 3. Can two different spin ...