Deformations of Clarke-Oliveira's Instantons on Bryant-Salamon $Spin(7)$-Manifold

In this paper we compute the deformations of Clarke-Oliveira’s instantons on the Bryant-Salamon $Spin(7)$-Manifold. The Bryant-Salamon $Spin(7)$-Manifold – the negative spinor bundle of $S^4$ – is an asymptotically conical manifold where the link is the squashed $7$-sphere. We use the deformation theory developed by the author in a previous paper to calculate the deformations of Clarke-Oliveira’s instantons and calculate the virtual dimensions of the moduli spaces.