Johannes Nordström, Imperial College London and University of Bath
“A new invariant of G2-structures”
In joint work with Diarmuid Crowley, we introduce a Z/48-valued invariant of G2-structures on closed 7-manifolds, defined in terms of the signature and Euler characteristic of a cobound- ary with Spin(7)-structure. The problem of deciding for which 7-manifolds the invariant clas- sifies G2-structures up to homotopies and diffeomorphisms is closely related to counting the number of different smooth structures on a 7-manifold. For the examples of holonomy G2 metrics on diffeomorphic closed manifolds exhibited by Corti, Haskins, Pacini and myself, the associated G2-structures are homotopic because they have the same invariant.