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Semi-Free Actions with Manifold Orbit Spaces

John Harvey Orcid Logo, Martin Kerin, Krishnan Shankar

Documenta Mathematica: Journal der Deutschen Mathematiker-Vereinigung, Volume: 25, Pages: 2085 - 2114

Swansea University Author: John Harvey Orcid Logo

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DOI (Published version): 10.25537/dm.2020v25.2085-2114

Abstract

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 fixedpoint components of codimension 4 are connecte...

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Published in: Documenta Mathematica: Journal der Deutschen Mathematiker-Vereinigung
ISSN: 1431-0643e 1431-0635
Published: Deutsche Mathematiker-Vereinigung e.V., Berlin 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa56479
Abstract: 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 fixedpoint components of codimension 4 are connected sums of S^3-bundles over S^2. 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 S^3 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 Description: Final published version is available at https://elibm.org/article/10012075.
Keywords: circle action, semi-free action, 5-manifolds, 4-manifolds, 8-manifolds
College: Faculty of Science and Engineering
Start Page: 2085
End Page: 2114

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