Twisted Borel K-theory and generalizations

• Grant number: 23/03876-6
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: March 01, 2024
• End date: February 28, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Fabio Ferrari Ruffino
• Grantee: Gabriel Longatto Clemente
• Supervisor: José María Cantarero López
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Institution abroad: Centro de Investigación en Matemáticas A.C., Mérida (CIMAT), Mexico
• Associated to the scholarship: 22/00676-3 - Differential Singular Homology, BP.DR

Abstract

The present project is the natural continuation of the one realized by the former Ph.D. student Alffer Gustavo Hernandez Posada, who computed some interesting twisted K-theory groups up to extension, i.e. he showed that they are the central term of a certain short exact sequence. This is a meaningful result, but it has to be completed by computing the groups themselves, not only up to extension. Moreover, these computations have been realized in the topological framework, and we aim to extend them to the differential setting. (AU)