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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Circle actions on simply connected $4$-manifolds

Author: Ronald Fintushel
Journal: Trans. Amer. Math. Soc. 230 (1977), 147-171
MSC: Primary 57E25
MathSciNet review: 0458456
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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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Keywords: Group action, 4-manifold, orbit space, equivariant homeomorphism, equivariant plumbing, quadratic form
Article copyright: © Copyright 1977 American Mathematical Society