On modular homology of simplicial complexes: Shellability

For a simplicial complex ii and coefficient domain F let F Delta be the F-module with basis Delta. We investigate the inclusion map given by partial derivative:tau -->sigma (1) + sigma (2) + sigma (3) + ...+ sigma (k) which assigns to every face tau the sum of the co-dimension 1 faces contained In tau. When the coefficient domain is a field of characteristic p>0 this map gives rise to homological sequences. We investigate this modular homology for shellable complexes. (C) 2001 Academic Press.