Semi-free actions with manifold orbit spaces

Harvey, John ORCID: https://orcid.org/0000-0001-9211-0060, Kerin, Martin and Shankar, Krishnan 2020. Semi-free actions with manifold orbit spaces. Documenta Mathematica Vol 25 , pp. 2085-2114. 10.25537/DM.2020V25.2085-2114

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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.

Item Type:	Article
Status:	Published
Schools:	Schools > Mathematics
Publisher:	Universität Bielefeld
ISSN:	1431-0635
Date of First Compliant Deposit:	3 August 2022
Last Modified:	14 May 2023 16:34
URI:	https://orca.cardiff.ac.uk/id/eprint/150997

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