Geodesic
Lefschetz properties and basic constructions on simplicial spheres
Journal of Algebraic Combinatorics, Tome 31 (2010) no. 1, pp. 111-129.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The well known $g$-conjecture for homology spheres follows from the stronger conjecture that the face ring over the reals of a homology sphere, modulo a linear system of parameters, admits the strong-Lefschetz property. We prove that the strong-Lefschetz property is preserved under the following constructions on homology spheres: join, connected sum, and stellar subdivisions. The last construction is a step towards proving the $g$-conjecture for piecewise-linear spheres.
Keywords: keywords face ring, strong-Lefschetz property, homology sphere 
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     title = {Lefschetz properties and basic constructions on simplicial spheres},
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Babson, Eric; Nevo, Eran. Lefschetz properties and basic constructions on simplicial spheres. Journal of Algebraic Combinatorics, Tome 31 (2010) no. 1, pp. 111-129. http://geodesic.mathdoc.fr/item/JAC_2010__31_1_a3/