IJPAM: Volume 21, No. 3 (2005)

ON CERTAIN RELATIVE COHOMOLOGICAL INVARIANTS

Maria Gorete Carreira Andrade$^1$,
Ermínia de Lourdes Campello Fanti$^2$, Janey Antonio Daccach$^3$
$^{1,2}$Departamento de Matemática
Instituto de Biociências, Letras e Ciências Exatas (IBILCE)
Universidade Estadual Paulista (UNESP)
R. Cristovão Colombo, 2265 - Jardim Nazareth
CEP 15.054-000, São José do Rio Preto, SP, BRAZIL
$^1$e-mail: gorete@ibilce.unesp.br;
$^2$e-mail: fanti@ibilce.unesp.br
$^3$Instituto de Ciências Matemáticas e de Computação (ICMC)
Universidade de São Paulo
Av. Trabalhador São-Carlense, 400 - Centro
Caixa Postal: 668 - CEP: 13560-970 - São Carlos - SP, BRASIL
e-mail: janey@icmc.sc.usp.br


Abstract.In this work we study general properties of the invariant end $E(G, {\mathcal S}, M)$, where $G$ is a group, ${\mathcal S}$ is a family of subgroups with infinite index in $G$ and M is a $\mathbb{Z}_2 G$-module. When $M = \mathbb{Z}_2 G \otimes_{\mathbb{Z}_2 S}\overline{\mathbb{Z}_2 S}$ and ${\mathcal S} = \{S\}$, we denote $E(G, \{S\},\mathbb{Z}_2 G \otimes_{\mathbb{Z}_2 S}\overline{\mathbb{Z}_2 S})$ by $\Et$. Using the theory of cohomology of groups, we study $\Et$ and its relations with the ends $e(G)$ (defined by Hopf and Specker), $\ \e $ (due to Houghton and Scott) and $ \ \et$ (defined by Kropholler and Roller). We also obtain some results about duality of groups.

Received: May 2, 2005

AMS Subject Classification: 20J06, 55M05, 20E06

Key Words and Phrases: cohomology of groups, ends of pairs of groups, duality, Eilenberg-Maclane spaces

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 21
Issue: 3