The FPm conjecture for betabelian groups in small dimensions

• Grant number: 06/00978-7
• Support Opportunities: Scholarships in Brazil - Master
• Start date: November 01, 2006
• End date: July 31, 2008
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Dessislava Hristova Kochloukova
• Grantee: Daniel Cariello
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The homological invariant Sigma^1(G), where G is afinitely generated metabelian group, was used to classify finitely presentable metabelian groups. The description of such groups was based in the geometric properties of Sigma^1(G). The FPm-Conjecture relates geometric properties of this invariant with the homological type FPm of G. The FP3-Conjecture was proved when G is a split extension of abelian groups. Algebric and geometric methods were used in this proof. The proposal of this work is to simplify the proof of FP3-Conjecture for discrete groups and if it is possible to generalize for dimension 4 (thus proving the FP4-Conjecture in the split extension case).

Academic Publications

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

CARIELLO, Daniel. The FPm conjecture for betabelian groups in small dimensions. 2008. Master's Dissertation - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.