Fixed points and coincidences in differential topology

• Grant number: 09/52017-9
• Support Opportunities: Regular Research Grants
• Start date: August 01, 2009
• End date: August 31, 2010
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Agreement: DFG
• Principal Investigator: Daciberg Lima Gonçalves
• Grantee: Daciberg Lima Gonçalves
• Principal researcher abroad: Ulrich Koschorke
• Institution abroad: University of Siegen, Germany
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This project consist mainly in study several questions about coincidence in positive codimension. One of the problems is study the self coincidence of maps between spheres. The relation with the Kervaire invariant problem is explored. Another major problem is the study of fibre preserving maps. Here one should classify the set of fiber preserving maps of some families of bundles(like torus bundles over a surface) and compute the Normal bordism invariants which detect coincidence. (AU)