Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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A compact non-formal closed G_2 manifold with b_1=1

Lucía Martín Merchán

created by daniele on 05 Oct 2021
modified on 13 Nov 2021

23 nov 2021 -- 14:30

DIMaI, Firenze (online)

Seminario di Geometria Differenziale e Analisi Complessa del Dipartimento di Matematica e Informatica "Ulisse Dini" dell'Università di Firenze


A G2 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 G2 structure is torsion-free if φ is parallel, closed if φ is closed and cocalibrated if φ is co-closed. This talk contributes to understanding topological properties of compact manifolds with a closed G2 structure that cannot be endowed with any torsion-free G2 structure. Namely, we construct such a manifold that is non-formal and has first Betti number b1=1. The starting point is a nilmanifold (M,φ) with a closed G2 structure that admits an involution preserving φ such that the quotient M/Z2 is a non-formal orbifold with b1=1. Then we perform a resolution of these singularities obtaining a manifold endowed with a closed G2 structure; we finally prove that the resolution verifies the same topological properties and do not admit any torsion-free G2 structure.

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