Algebra Seminar 

30/11/2006, 15:00 — 16:00 — Room P4.35, Mathematics Building
Shoham Shamir, Aberdeen Topology Center

Cellular Approximations and the Eilenberg-Moore Spectral Sequence

Given $R$-modules $k$ and $M$, a $k$-cellular approximation to $M$ is the "closest approximation" of $M$ that can be built from $k$ using homotopy colimits. The results of Dwyer, Greenlees and Iyengar show the target of the Eilenberg-Moore cohomology spectral sequence for a fibration has a natural interpretation as a certain $k$-cellular approximation. I will introduce the concept of cellular approximations and show how they can be applied to give new proofs for known convergence results of the Eilenberg-Moore spectral sequence and generalize another.