BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lucía Martín Merchán DTSTART:20211123T133000Z DTEND:20211123T143000Z DTSTAMP:20260423T024506Z UID:GeoSem/31 DESCRIPTION:Title: A compact non-formal closed G_2 manifold with b_1=1\nby Lucía Martí n Merchán as part of Geometry Seminar - University of Florence\n\n\nAbstr act\nA G_2 structure on a 7-dimensional Riemannian manifold determined by a certain type of 3-form φ. These are classified into 16 types according to PDEs involving φ\; for instance\, the G_2 structure is torsion-free if φ is parallel\, closed if φ is closed and cocalibrated if φ is co-cl osed.\nThis talk contributes to understanding topological properties of co mpact manifolds with a closed G_2 structure that cannot be endowed with an y torsion-free G_2 structure. Namely\, we construct such a manifold that i s non-formal and has first Betti number b_1=1. The starting point is a nil manifold (M\,φ) with a closed G_2 structure that admits an involution pre serving φ such that the quotient M/Z_2 is a non-formal orbifold with b_1 =1. Then we perform a resolution of these singularities obtaining a manifo ld endowed with a closed G_2 structure\; we finally prove that the resolut ion verifies the same topological properties and do not admit any torsion- free G_2 structure.\n LOCATION:https://researchseminars.org/talk/GeoSem/31/ END:VEVENT END:VCALENDAR