Hodge theory: De Rham cohomology and an introduction to Complex Geometry

• Grant number: 14/06913-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): August 01, 2014
• Effective date (End): July 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Henrique Nogueira de Sá Earp
• Grantee: Leonardo Francisco Cavenaghi
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The objective of project is to formulate and prove the Hodge theorem. Discussed topics include differentiable manifolds, the de Rham cohomology, integration of forms, forms on manifolds, Laplace operators and a brief introduction to Kahler manifolds. (AU)