About some theories of cohomology groups and applications

Author(s)

Jessica Cristina Rossinati Rodrigues da Costa

• Document type: Master's Dissertation
• Press: São José do Rio Preto. 2016-03-29.
• Institution: Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto
• Defense date: 2016-03-02
• Advisor: Maria Gorete Carreira Andrade

Abstract

In this work we present a study of the ordinary cohomology of groups, Tate cohomology and Farrell cohomology, and some applications in the context of Algebraic Topology. In this context we were developed topics of the theory of groups with periodic cohomology, detailing results and necessary and sufficient conditions for a group to have this property. As an application of this theory we present a criterion for a map defined in sphere homotopy in a CW-complex to have a (H,G)-coincidence. Also, we have developed some topics about groups that satisfy certain finiteness conditions, as for example, virtual duality groups. Besides, through Farrell cohomology, we present an obstruction for virtual duality groups satisfying the duality isomorphism of the theory due to Bieri and Eckmann. (AU)

• FAPESP's process: 13/23980-0 - On certain theories of cohomology of groups and applications
• Grantee: Jéssica Cristina Rossinati Rodrigues da Costa
• Support Opportunities: Scholarships in Brazil - Master