In the following we show that a Stein filling S of the 3-torus T^3 is homeomorphic to D^2 \times T^2. In the proof we also show that if S is Stein and \partial S is diffeomorphic to the Seifert fibered 3-manifold -\Sigma (2,3,11) then b_1(S)=0 and Q_S=H. Similar results are obtained for the Poincaré homology sphere \pm \Sigma (2,3,5); in studying these fillings we apply recent gauge theoretic results, and prove our theorems by determining certain Seiberg-Witten invariants.
STIPSICZ, ANDRAS I. (2002) "Gauge theory and Stein fillings of certain 3-manifolds," Turkish Journal of Mathematics: Vol. 26: No. 1, Article 9. Available at: https://journals.tubitak.gov.tr/math/vol26/iss1/9