Topology and invariants of maps between varieties

• Grant number: 18/07040-1
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: July 01, 2018
• End date: July 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Marcelo José Saia
• Grantee: Marcelo José Saia
• Visiting researcher: Jean-Paul Michel Ildephonse Brasselet
• Visiting researcher institution: Institut National des Sciences Mathématiques et de Leurs Interactions (INSMI) , France
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• City of the host institution: São Carlos
• Associated research grant: 14/00304-2 - Singularities of differentiable mappings: theory and applications, AP.TEM

Abstract

The main theme addressed in the research projects that Professor Jean-Paul has developed with several researchers in the area of Singularities in Brazil is the description of topological and geometric properties of applications between varieties. One of the most used methods to understand these properties is the determination of numeric, algebraic and topological invariants associated with the singularities of these applications. Among the works that Professor Jean-Paul has collaborated with researchers in Brazil, we highlight the following: Study of methods and invariants that allow the determination of classes of bordismo. We intend to study methods and invariants to detect the orientated bordibl class of a codimension two immersion using Thom's polynomial. The purpose of this paper is to study the following question: If two germs of analytic spaces are bi-Lipschitz equivalents, what can be said about their Nash modifications? Are they at least homeomorphic? A positive answer to this question leads to the conclusion that Euler's obstruction is a bi-Lipschitz invariant. (AU)