Discrete CATS Seminar
####
**
**#####
U N I V E R S I T Y
O F
K E N T U C K Y

DISCRETE
CATS
SEMINAR

WHERE CATS =
COMBINATORICS,
ALGEBRA,
TOPOLOGY
&
STATISTICS!

845 PATTERSON OFFICE TOWER

SPRING 2010

##
"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.