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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Vespri, Vincenzo / Marano, Salvatore Angelo


IMPACT FACTOR 2018: 0.726
5-year IMPACT FACTOR: 0.869

CiteScore 2018: 0.90

SCImago Journal Rank (SJR) 2018: 0.323
Source Normalized Impact per Paper (SNIP) 2018: 0.821

Mathematical Citation Quotient (MCQ) 2018: 0.34

ICV 2018: 152.31

Open Access
Online
ISSN
2391-5455
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Volume 13, Issue 1

Issues

Volume 13 (2015)

On Poincaré duality for pairs (G,W)

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
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ 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
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Lígia Laís Fêmina
Published Online: 2015-05-28 | DOI: https://doi.org/10.1515/math-2015-0035

Abstract

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.

Keywords: Poincaré duality pairs; Cohomology of groups; Cohomological invariants

MSC: 20J05, 55P20, 55U30

References

  • [1] Andrade, M.G.C., Fanti, E.L.C., A relative cohomological invariant for pairs of groups, Manuscripta Math., 1994, 83, 1-18. CrossrefGoogle Scholar

  • [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. Google Scholar

  • [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. Google Scholar

  • [4] Bieri, R., Eckmann, B., Relative homology and Poincaré duality for group pairs, J. Pure Appl. Algebra, 1978, 13, 277-319. CrossrefGoogle Scholar

  • [5] Brown, K.S., Cohomology of groups, Grad. Texts in Mat. 87, Springer, Berlin-New York-Heidelberg, 1982. Google Scholar

  • [6] Dicks, W., Dunwoody, M. J., Groups acting on graphs, Cambridge University Press, Cambridge, 1989. Google Scholar

  • [7] Kropholler, P. H., Roller, M. A., Splittings of Poincaré duality groups II, J. Lond. Math. Soc., 1988, 38, 410-420. Google Scholar

  • [8] Weiss, E., Cohomology of Groups, Academic Press Inc., New York, 1969. Google Scholar

About the article

Received: 2014-05-02

Accepted: 2015-02-03

Published Online: 2015-05-28


Citation Information: Open Mathematics, Volume 13, Issue 1, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0035.

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©2015 Maria Gorete Carreira Andrade et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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[1]
Maria Gorete Carreira Andrade and Ermínia de Lourdes Campello Fanti
Topology and its Applications, 2018

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