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Mathematica Slovaca

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Volume 64, Issue 3


Low-dimensional topology and ordering groups

Dale Rolfsen
Published Online: 2014-07-05 | DOI: https://doi.org/10.2478/s12175-014-0228-4


This expository paper explores the interaction of group ordering with topological questions, especially in dimensions 2 and 3. Among the topics considered are surfaces, braid groups, 3-manifolds and their structures such as foliations and mappings between them. A final section explores currently ongoing research regarding spaces of homeomorphisms and their orderability properties. This is not meant to be a comprehensive survey, but rather just a taste of the rich relationship between topology and the theory of ordered groups.

MSC: Primary 06F15, 20F60; Secondary 57M07, 57M27

Keywords: group ordering; manifold; surface; braid group; foliation

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About the article

Published Online: 2014-07-05

Published in Print: 2014-06-01

Citation Information: Mathematica Slovaca, Volume 64, Issue 3, Pages 579–600, ISSN (Online) 1337-2211, DOI: https://doi.org/10.2478/s12175-014-0228-4.

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© 2014 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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