Vol. 109, No. 2, 1983

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Compact connected Lie groups acting on simply connected 4-manifolds

Hae Soo Oh

Vol. 109 (1983), No. 2, 425–435

Suppose a compact connected Lie group G acts effectively on a simply connected 4-manifold M. Then we show that G is one of the groups SO(5), SU(3)∕Z(G), SO(3) × SO(3), SO(4), SO(3) ×T1, (SU(2) ×T1)∕D, SU(2), SO(3), T2, T1, and that the representatives of the conjugacy classes of the principal isotropy groups for these groups on M are, respectively, SO(4), U(2), T2, SO(3), S1, S1, SO(2) or e, SO(2) or D2n, e, and e. We also show that in each of these cases M is a connected sum of copies of S4, S2 × S2, CP2, and CP2 (except when G is T1, see Theorem 2.6).

Mathematical Subject Classification 2000
Primary: 57S15
Secondary: 57S25
Received: 11 May 1981
Published: 1 December 1983
Hae Soo Oh