Torus actions on simply connected 4-manifolds
In this paper, we study smooth effective actions of the 2-dimensional torus group T 2 ~= SO(2)xSO(2) on simply connected, closed 4-dimensional manifolds. Using the conical orbit space of the quotient, a cross-sectioning theorem for the orbit map p : M ? M/G is achieved. An equivariant classification theorem is obtained as an application of the cross- sectioning theorem; it is shown that such a manifold is S4, S2 x S2, CP2, or CP2, that is,CP2 with the reverse orientation, or an equivariant connected sum of S2 x S2, CP2, or CP2 up to equivariant diffeomorphism. The decompositions are not unique.