ASD deformation complex
= ASD deformation complex
{c}
{title2=$D_A=d_A^*\oplus d_A^+$}
The infinitesimal gauge and curvature complex is $0\to\Omega^0(\operatorname{ad}E)\xrightarrow{d_A}\Omega^1(\operatorname{ad}E)\xrightarrow{d_A^+}\Omega^{2,+}(\operatorname{ad}E)\to0$. Its composite on $\xi$ is $[F_A^+,\xi]=0$. Its cohomology describes infinitesimal stabilizers, deformations and obstructions. The gauge-fixed operator is $D_A=d_A^*\oplus d_A^+$.
// Destination: geometry-and-topology.bigb