Circle actions on simply connected 4-manifolds

Fintushel, Ronald

doi:10.1090/S0002-9947-1977-0458456-6

Circle actions on simply connected $4$-manifolds
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Trans. Amer. Math. Soc. 230 (1977), 147-171 Request permission

Abstract:

Locally smooth ${S^1}$-actions on simply connected 4-manifolds are studied in terms of their weighted orbit spaces. An equivariant classification theorem is proved, and the weighted orbit space is used to compute the quadratic form of a given simply connected 4-manifold with ${S^1}$-action. This is used to show that a simply connected 4-manifold which admits a locally smooth ${S^1}$-action must be homotopy equivalent to a connected sum of copies of ${S^4},C{P^2}, - C{P^2}$, and ${S^2} \times {S^2}$.

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Groups on

with principal orbits of dimension

4

23

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