NIELSEN THEORY FOR MAPS BETWEEN SPHERICAL 3-MANIFOLDS AND SOME HOMOGENEOUS SPACES

• Grant number: 23/16051-5
• Support Opportunities: Regular Research Grants
• Start date: February 01, 2024
• End date: May 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Daciberg Lima Gonçalves
• Grantee: Daciberg Lima Gonçalves
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The project has two goals on the doamin of fixed point theory. The first consists of classifying for each pair of spherical manifolds of dimension 3 the set of homotopy classes between them. Then for each pair of such homotopy classes determine the invariants Reidemeister classes, índices of the the Nielsen classes and Nielsen number. The second study the homogeneous spaces of the unitary group U(n) in relation to the property R-infinity, i.e. every homotopy equivalence has an infinite Reidemeistar number. (AU)