On Poincaré duality for pairs (G,W)

• Autorzy: Maria Gorete Carreira Andrade , Ermínia de Lourdes Campello Fanti , Lígia Laís Fêmina
• Języki publikacji: EN

Abstrakty

EN

Let G be a group and W a G-set. In this work we prove a result that describes geometrically, for a Poincaré duality pair (G, W ), the set of representatives for the G-orbits in W and the family of isotropy subgroups. We also prove, through a cohomological invariant, a necessary condition for a pair (G, W ) to be a Poincaré duality pair when W is infinite.

Słowa kluczowe

EN

Poincaré duality pairs; Cohomology of groups; Cohomological invariants

Kategorie tematyczne

• 55U30: Duality
• 55P20: Eilenberg-Mac Lane spaces
• 20J05: Homological methods in group theory

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2014-05-02

zaakceptowano

2015-02-03

online

2015-05-28

Twórcy

autor

Maria Gorete Carreira Andrade

• Departament of Mathematics - IBILCE - UNESP - São Paulo State
  University - Rua Cristovão Colombo, 2265, CEP 15054 - 000 - São José do Rio Preto - SP, Brazil

autor

Ermínia de Lourdes Campello Fanti

• Departament of Mathematics - IBILCE - UNESP - São Paulo State
  University - Rua Cristovão Colombo, 2265, CEP 15054 - 000 - São José do Rio Preto - SP, Brazil

autor

Lígia Laís Fêmina

• FAMAT - UFU - Av. João Naves de Avila, 2121, Uberlândia - MG - CEP: 38.408-100, Brazil

Bibliografia

• [1] Andrade, M.G.C., Fanti, E.L.C., A relative cohomological invariant for pairs of groups, Manuscripta Math., 1994, 83, 1-18. [Crossref]
• [2] Andrade, M.G.C., Fanti, E.L.C., Daccach, J. A., On certain relative invariants, Int. J. Pure Appl. Math., 2005, 21(3), 335-352.
• [3] Andrade, M.G.C., Fanti, E.L.C., Fêmina, L.L., Some remarks about Poincaré duality pairs, JP J. Geom. Topol., 2012, 12(2), 159-172.
• [4] Bieri, R., Eckmann, B., Relative homology and Poincaré duality for group pairs, J. Pure Appl. Algebra, 1978, 13, 277-319. [Crossref]
• [5] Brown, K.S., Cohomology of groups, Grad. Texts in Mat. 87, Springer, Berlin-New York-Heidelberg, 1982.
• [6] Dicks, W., Dunwoody, M. J., Groups acting on graphs, Cambridge University Press, Cambridge, 1989.
• [7] Kropholler, P. H., Roller, M. A., Splittings of Poincaré duality groups II, J. Lond. Math. Soc., 1988, 38, 410-420.
• [8] Weiss, E., Cohomology of Groups, Academic Press Inc., New York, 1969.

Identyfikatory

DOI

10.1515/math-2015-0035