Geometric structures on spheres and the Hopf conjecture

• Grant number: 22/09898-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2022
• End date: November 30, 2023
• 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

Abstract

This project aims to study the existence of complex and quasi-complex structures in unitary spheres and their relationship with parallelizable unitary spheres. It is also intended to study the historical development of Hopf's problem about the existence of a complex structure in S6. The materials used as a reference will be the articles "A Note on Kirchhoff's Theorem for Almost Complex Spheres I", by Lazaro O. R. Díaz, "On the History of the Hopf Problem", by Ilka Agricola et al., and "K-Theory and the Hopf Invariant" by John F. Adams and Michael F. Atiyah.(AU)