On certain homological invariant and its relation with Poincare duality pairs

Author(s)

Carreira Andrade, Maria Gorete ^[1] ; Gazon, Amanda Buosi ^[2] ; de Lima, Amanda Ferreira ^[2]

Affiliation

^[1] Univ Estadual Paulista, UNESP, Dept Matemat, Rua Cristovao Colombo 2265, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

^[2] UFSCAR Univ Fed Sao Carlos, Ctr Ciencias Exatas & Tecnol, Dept Estat, Rodovia Washington Luis, Km 235, BR-13565905 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: ALGEBRA & DISCRETE MATHEMATICS; v. 25, n. 2, p. 177-187, 2018.
• Web of Science Citations: 0

Abstract

Let G be a group, S = [S-i, i is an element of I] a non empty family of (not necessarily distinct) subgroups of infinite index in G and M a Z(2)G-module. In {[}4] the authors defined a homological invariant E,(G,S,M), which is ``dual{''} to the cohomological invariant E-{*}(G,S, M), defined in {[}1]. In this paper we present a more general treatment of the invariant E-{*}(G, S, M) obtaining results and properties, under a homological point of view, which are dual to those obtained by Andrade and Fanti with the invariant E(G, S, M). We analyze, through the invariant E-{*}(G, S, M), properties about groups that satisfy certain finiteness conditions such as Poincare duality for groups and pairs. (AU)

• FAPESP's process: 12/24454-8 - Algebraic, geometric and differential topology
• Grantee: Daciberg Lima Gonçalves
• Support Opportunities: Research Projects - Thematic Grants