Gorenstein rings through face rings of manifolds

Details Gorenstein rings through face rings of manifolds Gorenstein rings through face rings of manifolds

2008-06-05

arxiv.org/abs/0806.1017v1

Mathematics

Combinatorics

Scientific paper

The face ring of a homology manifold (without boundary) modulo a generic system of parameters is studied. Its socle is computed and it is verified that a particular quotient of this ring is Gorenstein. This fact is used to prove that the sphere $g$-conjecture implies all enumerative consequences of its far reaching generalization (due to Kalai) to manifolds. A special case of Kalai's manifold $g$-conjecture is established for homology manifolds that have a codimension-two face whose link contains many vertices.

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