Semi-Free Actions with Manifold Orbit Spaces

Harvey, John; Kerin, Martin; Shankar, Krishnan

doi:10.25537/dm.2020v25.2085-2114

Semi-Free Actions with Manifold Orbit Spaces

Harvey, John; Kerin, Martin; Shankar, Krishnan

Authors

John Harvey

Dr Martin Kerin martin.p.kerin@durham.ac.uk
Assistant Professor

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