Classification of circle actions on -manifolds

Author:
Ronald Fintushel

Journal:
Trans. Amer. Math. Soc. **242** (1978), 377-390

MSC:
Primary 57S15

DOI:
https://doi.org/10.1090/S0002-9947-1978-0496815-7

MathSciNet review:
496815

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Abstract | References | Similar Articles | Additional Information

Abstract: This article studies locally smooth -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 where is the orbit space and 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:
https://doi.org/10.1090/S0002-9947-1978-0496815-7

Keywords:
4-manifold,
group action,
orbit space,
quadratic form

Article copyright:
© Copyright 1978
American Mathematical Society