"Balanced Buchsbaum* complexes"

Jonathan Browder
University of Washington

Thursday, June 10, 2010
11:00 am
745 POT

Abstract:

In the study of simplicial complexes, two of the most useful conditions on a complex are that it be Cohen-Macaulay (as are, for example, triangulations of spheres and balls) or Buchsbaum (all triangulations of manifolds, with or without boundary). Strengthening the Cohen-Macaulay property to that of double Cohen-Macaulayness yields many useful consequences, but the immediately analogous double-Buchsbaum property turns out to be in some ways weaker than one might like. Athanasiadis and Welker recently introduced a new manifold analogue of doubly Cohen-Macaulay complexes in the form of Buchsbaum* complexes, which have many useful properties similar to those of doubly CM complexes. This talk will give some background and basic results on Buchsbaum* complexes, and discuss how some of the properties of balanced doubly CM complexes have nice analogues for Buchsbaum* complexes.