A Richard Thompson group and its homotopical sigma invariant

Author(s)

Lonardo Rabelo

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2008-05-08

Examining board members

Dessislava Hristova Kochloukova; Ketty Abaroa de Rezende; Dacilberg Lima Gonçalves

• Advisor: Dessislava Hristova Kochloukova

Abstract

In this project we study one of the Richard Thompson's Group F e its Homotopical m-dimensional Sigma Invariant. The Richard Thompson Group F is very known by its interesting homological and homotopical properties, for example, it is of type FP8 ([04]). Also, F has the property of being defined in several distinct ways. The Sigma Invariant Theory was developed in last decades of twentieth century by R. Bieri, J. Groves, R. Geoghegan, H. Meinert, R. Strebel and others and is related to FPm properties of groups. The _1(F) was obtained in [03]. Recently the general case of _m(F) and _m(F, Z) (homotopical and homological versions, respectively), m = 2, were described by R. Bieri, R. Geoghegan and D. Kochloukova. Here, we present the homotopical version of this result (AU)

• FAPESP's process: 06/01872-8 - A homological invariant and Richard Thompson's group
• Grantee: Lonardo Rabelo
• Support Opportunities: Scholarships in Brazil - Master