Nu-invariant of G2-structures in (extra-)twisted connected sums

• Grant number: 24/22110-7
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: September 01, 2025
• End date: January 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Henrique Nogueira de Sá Earp
• Grantee: Eduardo Toffolo
• Supervisor: Johannes Nordstrom
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: University of Bath, England
• Associated to the scholarship: 23/12359-5 - A homotopy invariant of G2-structures, BP.MS

Abstract

The candidate would like to visit Johannes Nordström at the University of Bath from 01/09/2025 to 31/01/2026 to discuss his article with Diarmuid Crowley New invariants of G_2-structures, which is central to the candidate's master's degree. In this paper, Crowley and Nordström define the nu-invariant and the xi-invariant of G_2-structures and demonstrate that these invariants classify all G_2-structure on 2-connected closed irreducible G_2-manifolds up to homotopy and diffeomorphism. Moreover, they compute several examples and show that the nu-invariant is always 24 for manifolds with G_2 holonomy obtained via the twisted connected sum construction, which is a significant method for constructing such objects.Furthermore, the candidate aims, if possible, to compute the value of the nu-invariant for some G_2-manifolds that have not yet been analysed. To achieve this, it is important to understand the extra-twisted connected sum, a method for constructing G_2-structures that offers a wider range of values for the nu-invariant compared to the simpler twisted connected sum. (AU)