June 6, 2022
TITLE: Computing \nu-invariants of Joyce’s G_2-manifolds
ABSTRACT: Crowley and Nordström introduced the \nu-invariant of a G_2-structure on a 7-manifold, taking values in the integers modulo 48. This invariant, and its spectral refinement due to Crowley, Goette and Nordström, has been important in understanding the connected components of G_2 metric moduli spaces. In this talk I explain how to compute the \nu-invariant for many of the closed torsion-free G_2-manifolds defined by Joyce’s generalized Kummer construction.