In the following we show that a Stein filling S of the 3-torus T3 is homeomorphic to D2 \times T2. In the proof we also show that if S is Stein and \partial S is diffeomorphic to the Seifert fibered 3-manifold -S (2,3,11) then b1(S)=0 and QS=H. Similar results are obtained for the Poincaré homology sphere \pm S (2,3,5); in studying these fillings we apply recent gauge theoretic results, and prove our theorems by determining certain Seiberg-Witten invariants.

In the following we show that a Stein filling S of the 3-torus T3 is homeomorphic to D2 \times T2. In the proof we also show that if S is Stein and \partial S is diffeomorphic to the Seifert fibered 3-manifold -S (2,3,11) then b1(S)=0 and QS=H. Similar results are obtained for the Poincaré homology sphere \pm S (2,3,5); in studying these fillings we apply recent gauge theoretic results, and prove our theorems by determining certain Seiberg-Witten invariants.