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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.

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 …
Chris Gerig's user avatar
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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 …
Chris Gerig's user avatar
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0 votes
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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 …
Chris Gerig's user avatar
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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 …
Chris Gerig's user avatar
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