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7:38 AM
The tag now contains five questions.
2
Q: Understanding the Seiberg-Witten equations in dimension $3$

ParthaI am trying to understand the dimensional reduction of Seiberg-Witten equations from dimension $4$ to $3$, more specifically my concern is about ellipticity of the new equations in dimension $3$ under temporal gauge. I am reading the paper: https://arxiv.org/pdf/dg-ga/9606003.pdf. Look at lemma 1...

2
Q: Changing the sign of the moment map in the Seiberg Witten equations

user2271513The Seiberg-Witten equations on a closed four manifold $$ D_A \varphi = 0, F_A^+ = \mu(\varphi) $$ are elliptic (up to gauge transformations), and so the equations $$ D_A \varphi = 0, F_A^+ = -\mu(\varphi) $$ are also elliptic up to gauge transformations. Is anything known about the moduli space ...

4
Q: Taubes' SW$\Rightarrow$ Gr

ParthaI am reading Taubes' paper on SW$\Rightarrow$ Gr and lost in some analysis, can anyone help me to see how to get equation 2.19 from equation 2.18? Is this some version of Kato for the Laplacian?

1
Q: Question from Taubes' SW$\Rightarrow$ Gr

ParthaI am trying to understand Taubes' paper on SW$\Rightarrow$ Gr. I don't understand how either of the equations 2.16 or 2.17 appears, I would be happy to understand how the curvature term $F_a$ appears in equation 2.17.

0
Q: Positive mass theorem and Seiberg-Witten equations

ParthaApologies for not a very rigorous question. I came across this PhD thesis by XIAO ZHANG, a student of Yau. From the thesis: "We also investigate some basic facts on Spin$^c$ structure on $4$-dimensional manifolds, and define the hypersurface Spin$^c$ structure. For complete Riemannian $4$-dimensi...


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