Skip to main content Accessibility help
×
Home

COHEN–MACAULAY COMPLEXES AND KOSZUL RINGS

  • D. WOODCOCK (a1)

Abstract

Throughout this paper k denotes a fixed commutative ground ring. A Cohen–Macaulay complex is a finite simplicial complex satisfying a certain homological vanishing condition. These complexes have been the subject of much research; introductions can be found in, for example, Björner, Garsia and Stanley [6] or Budach, Graw, Meinel and Waack [7]. It is known (see, for example, Cibils [8], Gerstenhaber and Schack [10]) that there is a strong connection between the (co)homology of an arbitrary simplicial complex and that of its incidence algebra. We show how the Cohen–Macaulay property fits into this picture, establishing the following characterization.

A pure finite simplicial complex is Cohen–Macaulay over k if and only if the incidence algebra over k of its augmented face poset, graded in the obvious way by chain lengths, is a Koszul ring.

Copyright

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed