Simplicial complexes of small codimension

Abstract

We show that CM t \textrm {CM}_t simplicial complexes, a notion generalizing Buchsbaum-ness, of small codimension must have large depth, proving more precise results in the codimension 2 case. In the paper, we show that the CM t \textrm {CM}_t property is a topological invariant of a simplicial complex.