G2-instantons with symmetry [Geometry]

Gonçalo Oliveira (Duke University - E.U.A.)

G2-instantons, are 7-dimensional analogs of anti-self-dual connections in 4 dimensions, which however require the underlying manifold to have a so called G2-structure. The interest on these G2-instantons comes from the suggestion, of Donaldson and Segal, that it may be possible to use them to define enumerative invariants of G2-holonomy Riemannian metrics. In the talk, I will explain these ideas and report on joint work with Jason Lotay where we give existence, non-existence and classification results for these instantons. I will focus in the particular case of R4 x S3, with its two explicitly known distinct G2-holonomy metrics, and exhibit the different behavior of their instantons. I will also explain an explicit example of sequences of G2-instantons where “bubbling” and “removable singularity” phenomena occur in the limit. All this is joint work with Jason Lotay.

Room 6.2.33 [⤴]Fundação para a Ciência e Tecnologia