The Morse-Witten complex via spectral sequences

Author(s)

Ewerton Rocha Vieira

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2011-02-28

Examining board members

Ketty Abaroa de Rezende; Oziride Manzoli Neto; Mariana Rodrigues da Silveira

• Advisor: Ketty Abaroa de Rezende

Abstract

In this work, we study the Morse-Witten Complex via spectral sequences, using the connection matrix over z, which codi_es the connecting orbits of the Morse ow associated to the complex. The Sweeping Method algorithm applied to the connection matrix over z produces a spectral sequence (Er; rd), which in turn gives us important information on the dynamics. Given the need to compute the generators of Z-modules Erp,q and the diferentials drp,q of the spectral sequence, we use the software Sweeping Algorithm, calculates Erp,q and drp,q quickly and efficiently. We present a way to extend the Morse-Witten as [BaC1] and [BaC]. This complex exhibits information between non-consecutive critical points, not obtainable using the Morse-Witten complex. For this extended Morse Complex we also have an associated spectral sequence, whereby dynamical information is also obtained as in [BaC1] and [BaC] (AU)

• FAPESP's process: 09/12337-4 - The study of the Morse-Witten Complex via Spectral Sequences
• Grantee: Ewerton Rocha Vieira
• Support Opportunities: Scholarships in Brazil - Master