Differential Singular Homology

• Grant number: 22/00676-3
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: May 01, 2022
• End date: April 30, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Fabio Ferrari Ruffino
• Grantee: Gabriel Longatto Clemente
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated scholarship(s): 23/03876-6 - Twisted Borel K-theory and generalizations, BE.EP.DR

Abstract

The main aim of this project consists in the construction of a natural differential extension of singular homology, dualizing the analogous extension in the framework of cohomology. In particular, the groups we are going to define are supposed to fit in suitable exact sequences, analogous to the cohomological ones. Moreover, we expect that the corresponding version of Poincaré duality holds. Depending on the time left, it would be natural to investigate how to generalize the previous construction to any (co)homology theory.