Location: HH 312 Speaker: Lucia Martin Merchan (University of Waterloo)
Title: Closed G2 manifolds with low first Betti number via orbifold resolution techniques
A G2 structure on a 7-dimensional Riemannian manifold determined by a stable 3-form phi. These are classified into 16 types according to PDEs involving phi; for instance, the G2 structure is torsion-free if phi is parallel, closed if phi is closed and co-closed if phi is co-closed. This talk contributes to understanding the topological properties of compact manifolds with a closed G2 structure that cannot be endowed with any torsion-free G2 structure. Namely, we construct examples with low first Betti number and we analyze whether they are formal or not. For that, we develop techniques for resolving the singularities of closed G2 orbifolds that are global quotients M/Z2.