On certain theories of cohomology of groups and applications

• Grant number: 13/23980-0
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2014
• End date: February 29, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Maria Gorete Carreira Andrade
• Grantee: Jéssica Cristina Rossinati Rodrigues da Costa
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 12/24454-8 - Algebraic, geometric and differential topology, AP.TEM

Abstract

The goal of this project is, through the study of the ordinary cohomology of groups, Tate cohomology and Farrell cohomology to show applications in the context of Algebraic Topology. In this context will be studied topics of the theory of groups with periodic cohomology, detailing results and necessary and sufficient conditions for a group to have this property. Also, will be studied some topics about groups that satisfy certain finiteness conditions, as for example, virtual duality groups. Besides, through Farrell cohomology, will be present an obstruction for virtual duality groups satisfying the duality isomorphism of the theory due to Bieri and Eckmann.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

COSTA, Jéssica Cristina Rossinati Rodrigues da. About some theories of cohomology groups and applications. 2016. Master's Dissertation - Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto São José do Rio Preto.