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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
first_indexed 2021-03-22T10:24:00Z
last_indexed 2021-04-20T03:21:58Z
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spelling 2021-04-19T13:18:47.4182281 v2 56479 2021-03-22 Semi-Free Actions with Manifold Orbit Spaces 1a837434ec48367a7ffb596d04690bfd 0000-0001-9211-0060 John Harvey John Harvey true false 2021-03-22 MACS 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. Journal Article Documenta Mathematica: Journal der Deutschen Mathematiker-Vereinigung 25 2085 2114 Deutsche Mathematiker-Vereinigung e.V., Berlin 1431-0643e 1431-0635 circle action, semi-free action, 5-manifolds, 4-manifolds, 8-manifolds 26 2 2020 2020-02-26 10.25537/dm.2020v25.2085-2114 https://elibm.org/article/10012075 Final published version is available at https://elibm.org/article/10012075. COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2021-04-19T13:18:47.4182281 2021-03-22T10:11:33.5291184 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics John Harvey 0000-0001-9211-0060 1 Martin Kerin 2 Krishnan Shankar 3 56479__19682__62bb12791aea4db3bed228393f6865d9.pdf 56479.pdf 2021-04-19T13:13:22.4854595 Output 318672 application/pdf Version of Record true © 2020 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 4.0 (CC BY) License true eng http://creativecommons.org/licenses/by/4.0/
title Semi-Free Actions with Manifold Orbit Spaces
spellingShingle Semi-Free Actions with Manifold Orbit Spaces
John Harvey
title_short Semi-Free Actions with Manifold Orbit Spaces
title_full Semi-Free Actions with Manifold Orbit Spaces
title_fullStr Semi-Free Actions with Manifold Orbit Spaces
title_full_unstemmed Semi-Free Actions with Manifold Orbit Spaces
title_sort Semi-Free Actions with Manifold Orbit Spaces
author_id_str_mv 1a837434ec48367a7ffb596d04690bfd
author_id_fullname_str_mv 1a837434ec48367a7ffb596d04690bfd_***_John Harvey
author John Harvey
author2 John Harvey
Martin Kerin
Krishnan Shankar
format Journal article
container_title Documenta Mathematica: Journal der Deutschen Mathematiker-Vereinigung
container_volume 25
container_start_page 2085
publishDate 2020
institution Swansea University
issn 1431-0643e
1431-0635
doi_str_mv 10.25537/dm.2020v25.2085-2114
publisher Deutsche Mathematiker-Vereinigung e.V., Berlin
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url https://elibm.org/article/10012075
document_store_str 1
active_str 0
description 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.
published_date 2020-02-26T05:21:02Z
_version_ 1862961843206619136
score 11.102523

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