May 14, 2024
TITLE: G2-instantons over generalised Kummer constructions via finite group actions
ABSTRACT: This talk explanes a method for producing new examples of G2-instantons over generalised Kummer constructions. This method is based on an extension of Walpuski’s original gluing theorem for G2-instantons over generalised Kummer constructions and deforms a connection that is (in a quantified sense) close to being an instanton. The novelty compared to previous constructions is that we use finite group actions to overcome possible obstructions. More precisely, we choose the (pre-glued) almost-instanton to be invariant under such a group action. In order for the linear equation inside the fix-point iteration of the gluing theorem to be solvable, it then suffices that the invariant part of the cokernel of the linearised instanton operator vanishes (instead of the full cokernel). This allows for more general conditions on the gluing data than in previous constructions.
