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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Classification of circle actions on $ 4$-manifolds


Author: Ronald Fintushel
Journal: Trans. Amer. Math. Soc. 242 (1978), 377-390
MSC: Primary 57S15
MathSciNet review: 496815
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Abstract: This article studies locally smooth $ {S^1}$-actions on closed oriented 4-manifolds in terms of the orbit space, orbit type data, and the characteristic class of the action which lies in $ {H_1}({M^{\ast}},{S^{\ast}})$ where $ {M^{\ast}}$ is the orbit space and $ {S^{\ast}}$ is the image of a certain collection of singular orbits. It is proved that such actions are determined by their weighted orbit spaces and are in 1-1 correspondence with ``legally-weighted'' 3-manifolds. The information contained in the weighted orbit space is used to give a presentation of the fundamental group of the 4-manifold, and in certain cases the quadratic form is computed.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0496815-7
PII: S 0002-9947(1978)0496815-7
Keywords: 4-manifold, group action, orbit space, quadratic form
Article copyright: © Copyright 1978 American Mathematical Society