ASD deformation index ($\mathrm{ind}{D}_A=8k-3(1-b_1+b^{+})$)

For an $SU(2)$ bundle of charge $k$ on a closed oriented four-manifold, $\mathrm{ind}{D}_A=h_A^1-h_A^0-h_A^2=8k-3(1-b_1+b^{+})$. Equivalently it is $-2p_1(\mathrm{ad}E)[X]-3(\chi +\sigma )/2$, using $p_1(\mathrm{ad}E)=-4c_2(E)$. The Euler characteristic of the deformation complex has the opposite sign.

// Destination: analysis.bigb