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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access May 28, 2015

On Poincaré duality for pairs (G,W)

  • Maria Gorete Carreira Andrade , Ermínia de Lourdes Campello Fanti and Lígia Laís Fêmina
From the journal Open Mathematics

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.

References

[1] Andrade, M.G.C., Fanti, E.L.C., A relative cohomological invariant for pairs of groups, Manuscripta Math., 1994, 83, 1-18. 10.1007/BF02567596Search in Google 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. Search in 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. Search in Google Scholar

[4] Bieri, R., Eckmann, B., Relative homology and Poincaré duality for group pairs, J. Pure Appl. Algebra, 1978, 13, 277-319. 10.1016/0022-4049(78)90012-9Search in Google Scholar

[5] Brown, K.S., Cohomology of groups, Grad. Texts in Mat. 87, Springer, Berlin-New York-Heidelberg, 1982. 10.1007/978-1-4684-9327-6Search in Google Scholar

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

[7] Kropholler, P. H., Roller, M. A., Splittings of Poincaré duality groups II, J. Lond. Math. Soc., 1988, 38, 410-420. 10.1112/jlms/s2-38.3.410Search in Google Scholar

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

Received: 2014-5-2
Accepted: 2015-2-3
Published Online: 2015-5-28

©2015 Maria Gorete Carreira Andrade et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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