Selfintersection of immersions, via normal bordism

• Grant number: 11/13479-7
• Support Opportunities: Regular Research Grants
• Start date: October 01, 2011
• End date: September 30, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alice Kimie Miwa Libardi
• Grantee: Alice Kimie Miwa Libardi
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

The classical invariants to the existence of intersection of maps are defined in homology or cohomology groups. The intersection of maps was studied by us and by Koschorke, involving bordism of maps, in Conner and Floyd sense, allows us to intend to get an invariant to the existence of intersection of maps, lying in a particular normal bordism group, which is the strongest invariant, but very difficult to calculated. One goal of this project is to obtain conditions to the existence of intersection maps via an invariant in the bordism of maps, which is not so hard to define and to calculate them, also we will define the invariant in normal bordism group, compare them, by using our results. As a consequence we will study selfintersection of immersions, using results of papers in the reference. A study on immersions with non zero normal vector field will be developed, by using such technics. (AU)