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Semi-Free Actions with Manifold Orbit Spaces

Harvey, John; Kerin, Martin; Shankar, Krishnan

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Authors

John Harvey

Krishnan Shankar



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 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.

Citation

Harvey, J., Kerin, M., & Shankar, K. (2020). Semi-Free Actions with Manifold Orbit Spaces. Documenta Mathematica, 25, 2085-2114. https://doi.org/10.25537/dm.2020v25.2085-2114

Journal Article Type Article
Online Publication Date Nov 18, 2020
Publication Date 2020
Deposit Date Nov 15, 2022
Publicly Available Date Nov 15, 2022
Journal Documenta Mathematica
Publisher Documenta Mathematica
Peer Reviewed Peer Reviewed
Volume 25
Pages 2085-2114
DOI https://doi.org/10.25537/dm.2020v25.2085-2114
Publisher URL https://www.elibm.org/article/10012075
Related Public URLs https://orca.cardiff.ac.uk/id/eprint/150997

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