Global properties of a class of differential complexes

Author(s)

Hugo Cattarucci Botós

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2018-03-23

Examining board members

Sergio Luis Zani; Adalberto Panobianco Bergamasco; Cléber de Medeira; José Ruidival Soares dos Santos Filho

• Advisor: Sergio Luis Zani

Abstract

Consider the manifold Tn x S1 with coordinates (t;x) and let a(t) be a real and closed differential 1-form on Tn. In this work we consider the operator Lpsub>a = dt +a(t) Λ ∂x de D\'p from D\'p to D\'p+1, where D\'p is the space of all p-currents u = ∑ Ι I Ι = puI (t, x)dtI . The above operator defines a cochain complex consisting of the vector spaces D\'p and of the linear maps Lpa : D\'p → D\'p+1. We define what global solvability means for the above complex and characterize for which 1-forms a the complex is globally solvable. We will do the same with respect to global hypoellipticity on the first level of the complex. (AU)

• FAPESP's process: 16/06390-3 - Global solvability for a class of differential complexes
• Grantee: Hugo Cattarucci Botós
• Support Opportunities: Scholarships in Brazil - Master