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Results tagged with spin-geometry
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user 12310
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.
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votes
Accepted
Understanding the quadratic part in Seiberg Witten equation
So your $\phi$ in this special case really means $(\phi,0)$ in the direct sum, while $\psi$ means $(0,\psi)$. Then $q(\phi)$ is the 2x2 matrix with vanishing off-diagonal entries and nontrivial diagon …
- 17.5k
4
votes
Index of Modified Dirac Operator
Making my comment a formal answer:
The perturbation object is a compact operator (for any scaling $s$), and $D$ is Fredholm. The space of Fredholm operators is open in the (Banach) space of bounded li …
- 17.5k
4
votes
Accepted
Generalized geometry and spin structures
OK, I am making an assumption: I can re-interpret the problem (using the musical isomorphism) as $V$ being the diagonal embedding of $TM$ inside $TM\oplus TM$ and studying spin structures on them.
Ac …
- 17.5k
15
votes
Accepted
Meaning/origin of Seiberg-Witten equations/invariants
After thinking, and reading other references and re-reading the papers I mentioned, I may have found a sufficient explanation (at least to my care): Both instantons/monopoles are solutions to corresp …
- 17.5k