Diarmuid Crowley, Max Planck Institute for Mathematics
“A new invariant of G2 structures”
I will report on recent where we define an invariant of diffeomorphisms and homotopies of a G2 structure on a closed 7-manifold M. The ν-invariant takes values in Z/48 and is defined via the Euler characteristic and signature of a Spin(7)-coboundary of the G2 structure.
An important motivation for defining the ν-invariant is to investigate the connectivity of moduli space of G2-metrics on M in the case where such metrics exist.
I will discuss examples, calculations for the invariant to date and its relationship to the mapping class groups of spin 7-manifolds. This work is joint with Johannes Nordstr ̈om.
Please note special time