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Semi-Free Actions with Manifold Orbit Spaces

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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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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