Finite, Fiber- and Orientation-Preserving Group Actions on Totally Orientable Seifert Manifolds

In this paper we consider the finite groups that act fiber- and orientation-preservingly on closed, compact, and orientable Seifert manifolds that fiber over an orientable base space. We establish a method of constructing such group actions and then show that if an action satisfies a condition on th...

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Main Author:	Peet Benjamin
Format:	Article
Language:	English
Published:	Sciendo 2019-09-01
Series:	Annales Mathematicae Silesianae
Subjects:	geometry topology 3-manifolds finite group actions Seifert fibrations 57S25 55R05
Online Access:	http://www.degruyter.com/view/j/amsil.2019.33.issue-1/amsil-2019-0007/amsil-2019-0007.xml?format=INT

id	doaj-a070f478de8e4d5fb5ee131f93cf833b
record_format	Article
spelling	doaj-a070f478de8e4d5fb5ee131f93cf833b2020-11-24T22:26:11ZengSciendoAnnales Mathematicae Silesianae2391-42382019-09-0133123526510.2478/amsil-2019-0007amsil-2019-0007Finite, Fiber- and Orientation-Preserving Group Actions on Totally Orientable Seifert ManifoldsPeet Benjamin0Department of Mathematics, St. Martin’s University, Lacey, WA 98503, USAIn this paper we consider the finite groups that act fiber- and orientation-preservingly on closed, compact, and orientable Seifert manifolds that fiber over an orientable base space. We establish a method of constructing such group actions and then show that if an action satisfies a condition on the obstruction class of the Seifert manifold, it can be derived from the given construction. The obstruction condition is refined and the general structure of the finite groups that act via the construction is provided.http://www.degruyter.com/view/j/amsil.2019.33.issue-1/amsil-2019-0007/amsil-2019-0007.xml?format=INTgeometrytopology3-manifoldsfinite group actionsSeifert fibrations57S2555R05
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Peet Benjamin
spellingShingle	Peet Benjamin Finite, Fiber- and Orientation-Preserving Group Actions on Totally Orientable Seifert Manifolds Annales Mathematicae Silesianae geometry topology 3-manifolds finite group actions Seifert fibrations 57S25 55R05
author_facet	Peet Benjamin
author_sort	Peet Benjamin
title	Finite, Fiber- and Orientation-Preserving Group Actions on Totally Orientable Seifert Manifolds
title_short	Finite, Fiber- and Orientation-Preserving Group Actions on Totally Orientable Seifert Manifolds
title_full	Finite, Fiber- and Orientation-Preserving Group Actions on Totally Orientable Seifert Manifolds
title_fullStr	Finite, Fiber- and Orientation-Preserving Group Actions on Totally Orientable Seifert Manifolds
title_full_unstemmed	Finite, Fiber- and Orientation-Preserving Group Actions on Totally Orientable Seifert Manifolds
title_sort	finite, fiber- and orientation-preserving group actions on totally orientable seifert manifolds
publisher	Sciendo
series	Annales Mathematicae Silesianae
issn	2391-4238
publishDate	2019-09-01
description	In this paper we consider the finite groups that act fiber- and orientation-preservingly on closed, compact, and orientable Seifert manifolds that fiber over an orientable base space. We establish a method of constructing such group actions and then show that if an action satisfies a condition on the obstruction class of the Seifert manifold, it can be derived from the given construction. The obstruction condition is refined and the general structure of the finite groups that act via the construction is provided.
topic	geometry topology 3-manifolds finite group actions Seifert fibrations 57S25 55R05
url	http://www.degruyter.com/view/j/amsil.2019.33.issue-1/amsil-2019-0007/amsil-2019-0007.xml?format=INT
work_keys_str_mv	AT peetbenjamin finitefiberandorientationpreservinggroupactionsontotallyorientableseifertmanifolds
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Finite, Fiber- and Orientation-Preserving Group Actions on Totally Orientable Seifert Manifolds

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