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I define equations like the Seiberg-Witten equations for forms of a riemannian four-manifold $(M,g)$. $\alpha \in \Lambda_+ (TM)$ and $\theta \in \Lambda^1(TM)$. $$ d\alpha+\theta \wedge \alpha=0 $$ $$ d\theta_+=\frac{\alpha}{||\alpha ||} $$ The gauge group acts: $$ f.(\alpha,\theta)=(f\alpha,\theta- df/f) $$ Can we define invariants?

I define equations like the Seiberg-Witten equations for forms of a riemannian four-manifold $(M,g)$. $\alpha \in \Lambda^2 (TM)$ and $\theta \in \Lambda^1(TM)$. $$ d\alpha+\theta \wedge \alpha=0 $$ $$ d\theta_+=\frac{\alpha_+}{||\alpha ||} $$ The gauge group acts: $$ f.(\alpha,\theta)=(f\alpha,\theta- df/f) $$ Can we define invariants?

I define equations like the Seiberg-Witten equations for forms of a riemannian four-manifold $(M,g)$. $\alpha \in \Lambda^*(TM)$ and $\theta \in \Lambda^1(TM)$. $$ d\alpha+\theta \wedge \alpha=0 $$ $$ d\theta_+=0 $$ The gauge group acts: $$ f.(\alpha,\theta)=(f\alpha,\theta- df/f) $$ Can we define invariants?

I define equations like the Seiberg-Witten equations for forms of a riemannian four-manifold $(M,g)$. $\alpha \in \Lambda_+ (TM)$ and $\theta \in \Lambda^1(TM)$. $$ d\alpha+\theta \wedge \alpha=0 $$ $$ d\theta_+=\frac{\alpha}{||\alpha ||} $$ The gauge group acts: $$ f.(\alpha,\theta)=(f\alpha,\theta- df/f) $$ Can we define invariants?

I define equations like the Seiberg-Witten equations for forms of a riemannian four-manifold $(M,g)$. $\alpha \in \Lambda_+(TM)$ and $\theta \in \Lambda^1(TM)$. $$ d\alpha+\theta \wedge \alpha=0 $$ $$ d\theta_+=0 $$ The gauge group acts: $$ f.(\alpha,\theta)=(f\alpha,\theta- df/f) $$ Can we define invariants?

I define equations like the Seiberg-Witten equations for forms of a riemannian four-manifold $(M,g)$. $\alpha \in \Lambda^*(TM)$ and $\theta \in \Lambda^1(TM)$. $$ d\alpha+\theta \wedge \alpha=0 $$ $$ d\theta_+=0 $$ The gauge group acts: $$ f.(\alpha,\theta)=(f\alpha,\theta- df/f) $$ Can we define invariants?