A homotopy invariant of G2-structures

• Grant number: 23/12359-5
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2024
• End date: February 28, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Henrique Nogueira de Sá Earp
• Grantee: Eduardo Toffolo
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 21/04065-6 - BRIDGES: Brazil-France interplays in Gauge Theory, extremal structures and stability, AP.TEM
• Associated scholarship(s): 24/22110-7 - Nu-invariant of G2-structures in (extra-)twisted connected sums, BE.EP.MS

Abstract

This project aims to study the construction of the homotopic invariant \nu(\varphi) of a G_2-structure \varphi acting on the tangent bundle of a closed 7-manifold, as well as the demonstration that, for manifolds with G_2 holonomy obtained through a twisted connected sum, the associated torsion-free G_2-structure always has \nu(\varphi) = 24. We will also see the construction of the homotopic invariant \xi(\varphi), under the same previous conditions, and the result that, for 2-connected manifolds, the pair (\nu,\xi) determines a G_2-structure up to homotopy and diffeomorphism. Finally, some examples of G_2-structures and their respective invariant values will be studied.