Bi-Lipschitz invariant geometry

Author(s)

Thiago Filipe da Silva

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2018-01-18

Examining board members

Nivaldo de Góes Grulha Junior; Anne Frühbis krüger; Marcelo Escudeiro Hernandes; Miriam da Silva Pereira

• Advisor: Nivaldo de Góes Grulha Junior; Terence James Gaffney

Abstract

The study about bi-Lipschitz equisingularity has been a very important subject in Singularity Theory in last decades. Many different approach have cooperated for a better understanding about. One can see that the bi-Lipschitz geometry is able to detect large local changes in curvature more accurately than other kinds of equisingularity. The aim of this thesis is to investigate the bi-Lipschitz geometry in an algebraic viewpoint. We define some algebraic tools developing classical properties. From these tools, we obtain algebraic criterions for the bi-Lipschitz equisingularity of some families of analytic varieties. We present a categorical and homological viewpoints of these algebraic structure developed before. Finally, we approach algebraically the bi-Lipschitz equisingularity of a family of Essentially Isolated Determinantal Singularities. (AU)

• FAPESP's process: 13/22411-2 - Bi-Lipschitz Invariant Geometry
• Grantee: Thiago Filipe da Silva
• Support Opportunities: Scholarships in Brazil - Doctorate