My question is: I am request for the reference that Is there any relationship between the Seiberg-Witten Invariant and Donaldson's Invariant? Or the relationship between Seiberg-Witten Moduli Space and Yang-Mills Moduli space?
My question is a reference request.
My question is based on the following observation: For given compact smooth manifold M,
Consider the Seiberg-Witten Equation without perturbation, $F^+_A+(\phi \phi^*)_0$=0 $D_A^+ \phi =0$. Then every solution of the Seiberg-Witten Equation is a pair $(A, \phi)$, A is connection and $\phi$ is a spinor. However, for the reducible solution of Seiberg-Witten equation(the solution that $\phi=0$), we get the equation that $F_A^+$=0 An anti-selfdual equation of the curvature. When we change the orientation of the manifold M, all the Yang-Mills connection can be the antiself-dual. So I think in some way the Yang-Mills connection is the reducible solution of the Seiberg-Witten equation. Therefore, I believe there must be some strictly relationship between two manifold.
However, I ignore the difference of the $Spin^c$ structure and $SU(2)$, but I think with a proper choose of a Lie group homomorphism $f:SU(2)\rightarrow Spin^c$, we can map the Yang-Mills Moduli space into Seiberg-Witten Moduli space.
Maybe there exist some related questions in MO, but not what I want. Evans has asked a similar question:Is there a Seiberg-Witten version of Donaldson-Thomas theory?