Adapted splittings for pairs (G, W)

Author(s)

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

Affiliation

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

• Document type: Journal article
• Source: Topology and its Applications; v. 253, p. 17-24, FEB 15 2019.
• Web of Science Citations: 0

Abstract

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)

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