Adapted splittings for pairs (G, W)

Autor(es)

Carreira Andrade, Maria Gorete ^[1] ; Campello Fanti, Erminia de Lourdes ^[1]

Afiliação do(s) autor(es)

^[1] Sao Paulo State Univ, UNESP, IBILCE, Rua Cristovao Colombo 2265, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Topology and its Applications; v. 253, p. 17-24, FEB 15 2019.
• Citações Web of Science: 0

Resumo

Let G be a group, W a G-set with {[}G : G(w)] = infinity, for all w is an element of W, where G(w) denotes the point stabilizer of w is an element of W. Considering the restriction map res(W)(G) : H-1 (G, Z(2)G) -> Pi(w is an element of E) H-1 (G(w), Z(2)G), where E is a set of orbit representatives for the w E E G -action in W, we define an algebraic invariant denoted by (E) over bar (G, W). In this paper, by using the relation of this invariant with the end e(G) defined by Freudenthal-Hopf-Specker and a Swarup's Theorem about splittings of groups adapted to a family of subgroups, we show, for G finitely generated and W a G -set which falls into many finitely G -orbits, that (G, W) is adapted if, and only if, (E) over bar (G, W) >= 2. (C) 2018 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 12/24454-8 - Topologia algébrica, geométrica e diferencial
• Beneficiário: Daciberg Lima Gonçalves
• Modalidade de apoio: Auxílio à Pesquisa - Temático