Analytic Torsion and extensions for the Cheeger Müller theorem

Author(s)

Luiz Roberto Hartmann Júnior

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2009-12-10

Examining board members

Mauro Flávio Spreafico; Ryuichi Fukuoka; Caio Jose Colletti Negreiros; Pedro Luiz Queiroz Pergher; Maria Aparecida Soares Ruas

• Advisor: Mauro Flávio Spreafico
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Indexed in: Banco de Dados Bibliográficos da USP-DEDALUS; Biblioteca Digital de Teses e Dissertações - USP
• Location: Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação. Biblioteca Prof. Achille Bassi

Abstract

We study for Analytic Torsion of manifolds with boundary and also with conical singularities , more specifically, for a finite metric cone, with the purpose of investing the natural extension of the Cheeger Müller theorem for such spaces. we start by computing the Analytic Torsion of an any dimensional disc and of a manifold with totally boundary, by using geometric tools development by J. Brüning and X. Ma. Then, by using analytic tools development by M. Spreafico, we determine the Analytic Torsion of a cone over an odd dimensional sphere and we prove a theorem of Cheeger Müller type space. Moreover, we prove that the result of J. Brüning and X. Ma extends to the cone over an odd dimensional sphere (AU)

• FAPESP's process: 07/05452-6 - Torsion of spaces with a singularity of conical type
• Grantee: Luiz Roberto Hartmann Junior
• Support Opportunities: Scholarships in Brazil - Doctorate