Online Talk

Given a graded ring A, we want to know if it can be realized as the cohomology of a space X_A. We look at two cases of the problem:

orders (or muliplicatively closed lattices) in a rational exterior algebra and the graded Stanley-Reisner ring SR(K) corresponding to a simplicial complex K.  When all the generators are in degree 2 then we can construct  SR(K) as the cohomology of the Davis-Januszkiewicz space DJ(K). Other cases of the problem with larger degrees have been solved by Takeda. In this talk we will consider the case when the degrees are 4 and 6, and relate the problem to graph colouring.