Morse Index Stability for Yang–Mills Connections

Abstract We prove stability results for the Morse index plus nullity of Yang–Mills connections in dimension 4 under weak convergence. Precisely we establish that the sum of the Morse index and the nullity of a bounded sequence of Yang–Mills connections is asymptotically bounded above by the sum of the Morse index and the nullity of the weak limit and the bubbles, while the Morse index is asymptotically bounded below by the sum of the Morse index of the weak limit and the bubbles.