Improved almost Morawetz estimates for the cubic nonlinear Schrodinger equation

We prove global well-posedness for the cubic, defocusing, nonlinear Schr{"o}dinger equation on ${\mathbf{R}}^2$ with data $u_{0} \in H^{s}($\mathbf{R}$^{2})$,$s > 1/4$. We accomplish this by improving the almost Morawetz estimates in [9].