Semi-Free Actions with Manifold Orbit Spaces

Harvey, John; Kerin, Martin; Shankar, Krishnan

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
• Electronic ISSN: 1431-0643
• Publisher: Documenta Mathematica
• Peer Reviewed: Peer Reviewed
• Volume: 25
• Pages: 2085-2114
• DOI: https://doi.org/10.25537/dm.2020v25.2085-2114
• Public URL: https://durham-repository.worktribe.com/output/1186583
• Publisher URL: https://www.elibm.org/article/10012075
• Related Public URLs: https://orca.cardiff.ac.uk/id/eprint/150997