Title: Cohen-Macaulay and Gorenstein complexes from a topological 
       point of view
       
Author: Dietrich Notbohm

AMS Classification numbers: 13F55, 55R35

Address of Author: Dept. of Mathematics, University of Leicester, 
                   University Road, Leicester LE1 7RH, England
                   
Email address: dn8@mcs.le.ac.uk

Abstract:
The main invariant to study the combinatorics of a 
simplicial complex $K$ is the associated face ring or Stanley-Reisner algebra.
Reisner respectively Stanley explained in which sense 
Cohen-Macaulay and Gorenstein
properties of the face ring are reflected by geometric and/or 
combinatoric properties of the simplicial complex. We give a new proof for 
these result by homotopy theoretic methods and constructions. 
Our approach is based on 
 ideas used very successfully in the analysis of the homotopy theory
of classifying spaces.