Harvey, John and Kerin, Martin and Shankar, Krishnan (2020) 'Semi-Free Actions with Manifold Orbit Spaces.', Documenta Mathematica, 25 . pp. 2085-2114.
In this paper, we study smooth, semi-free actions on closed, smooth, simply connected manifolds, such that the orbit space is a smoothable manifold. We show that the only simply connected 5-manifolds admitting a smooth, semi-free circle action with fixed-point components of codimension 4 are connected sums of S3-bundles over S2. Furthermore, the Betti numbers of the 5-manifolds and of the quotient 4-manifolds are related by a simple formula involving the number of fixed-point components. We also investigate semi-free S3 actions on simply connected 8-manifolds with quotient a 5-manifold and show, in particular, that there are strong restrictions on the topology of the 8-manifold.
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||https://www.elibm.org/article/10012075|
|Date accepted:||No date available|
|Date deposited:||15 November 2022|
|Date of first online publication:||18 November 2020|
|Date first made open access:||15 November 2022|
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