Contractibility of the space of generic opers for classical groups

Abstract

Let $G$ be a reductive group and $X$ a smooth projective curve. We prove that, for $G$ classical and $\sigma$ an arbitrary $G$-local system on $X$, the space ${\overline{\mathrm{Op}}}_{G,\sigma }^{gen}$ of generic extended oper structures on $\sigma$ is homologically contractible. This contractibility result is crucial for the proof of the geometric Langlands conjecture.