The dynamic behind the spectral sequence

Author(s)

Mariana Rodrigues da Silveira

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2008-04-30

Examining board members

Ketty Abaroa de Rezende; Maria Alice Bertolim; Oziride Manzoli Neto; Marco Antonio Teixeira; Caio José Colletti Negreiros

• Advisor: Ketty Abaroa de Rezende

Abstract

In this work, we present an algorithm for a chain complex C and its di_erential given by a connection matrix _ which determines an associated spectral sequence (Er, dr). More specifically, a system spanning Er in terms of the original basis of C is obtained as well as the identi_cation of all di_erentials dr p : Er p ! Er p-r. In exploring the dynamical implication of a nonzero di_erential, we prove the existence of a path joining the singularities generating E0 p and E0 p-r in the case that a direct connection by a _ow line does not exist. This path is made up of juxtaposed orbits of the _ow and of the reverse _ow and which proves to be importantin some applications (AU)