On Poincaré duality for pairs (G,W)

Maria Gorete Carreira Andrade; Ermínia de Lourdes Campello Fanti; Lígia Laís Fêmina

Open Mathematics (2015)

  • Volume: 13, Issue: 1
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Maria Gorete Carreira Andrade, Ermínia de Lourdes Campello Fanti, and Lígia Laís Fêmina. "On Poincaré duality for pairs (G,W)." Open Mathematics 13.1 (2015): null. <http://eudml.org/doc/270926>.

@article{MariaGoreteCarreiraAndrade2015,
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.},
author = {Maria Gorete Carreira Andrade, Ermínia de Lourdes Campello Fanti, Lígia Laís Fêmina},
journal = {Open Mathematics},
keywords = {Poincaré duality pairs; Cohomology of groups; Cohomological invariants},
language = {eng},
number = {1},
pages = {null},
title = {On Poincaré duality for pairs (G,W)},
url = {http://eudml.org/doc/270926},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Maria Gorete Carreira Andrade
AU - Ermínia de Lourdes Campello Fanti
AU - Lígia Laís Fêmina
TI - On Poincaré duality for pairs (G,W)
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - null
AB - 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.
LA - eng
KW - Poincaré duality pairs; Cohomology of groups; Cohomological invariants
UR - http://eudml.org/doc/270926
ER -

References

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  1. [1] Andrade, M.G.C., Fanti, E.L.C., A relative cohomological invariant for pairs of groups, Manuscripta Math., 1994, 83, 1-18. [Crossref] Zbl0837.20061
  2. [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. Zbl1121.20038
  3. [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. Zbl1262.20055
  4. [4] Bieri, R., Eckmann, B., Relative homology and Poincaré duality for group pairs, J. Pure Appl. Algebra, 1978, 13, 277-319. [Crossref] Zbl0392.20032
  5. [5] Brown, K.S., Cohomology of groups, Grad. Texts in Mat. 87, Springer, Berlin-New York-Heidelberg, 1982. 
  6. [6] Dicks, W., Dunwoody, M. J., Groups acting on graphs, Cambridge University Press, Cambridge, 1989. Zbl0665.20001
  7. [7] Kropholler, P. H., Roller, M. A., Splittings of Poincaré duality groups II, J. Lond. Math. Soc., 1988, 38, 410-420. Zbl0687.20045
  8. [8] Weiss, E., Cohomology of Groups, Academic Press Inc., New York, 1969. Zbl0192.34204

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