The number of locally invariant orderings of a group Article Swipe
Idrissa Bâ
,
Adam Clay
,
Ian M. Thompson
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2204.00766
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2204.00766
We show that if a nontrivial group admits a locally invariant ordering, then it admits uncountably many locally invariant orderings. For the case of a left-orderable group, we provide an explicit construction of uncountable families of locally invariant orderings; for a general group we provide an existence theorem that applies compactness to yield uncountably many locally invariant orderings. Along the way, we define and investigate the space of locally invariant orderings of a group, the natural group actions on this space, and their relationship to the space of left-orderings.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2204.00766
- https://arxiv.org/pdf/2204.00766
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
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All OpenAlex metadata
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https://doi.org/10.48550/arxiv.2204.00766Digital Object Identifier
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The number of locally invariant orderings of a groupWork title
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preprintOpenAlex work type
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enPrimary language
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2022Year of publication
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2022-04-02Full publication date if available
- Authors
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Idrissa Bâ, Adam Clay, Ian M. ThompsonList of authors in order
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https://arxiv.org/abs/2204.00766Publisher landing page
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https://arxiv.org/pdf/2204.00766Direct link to full text PDF
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2204.00766Direct OA link when available
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Uncountable set, Invariant (physics), Mathematics, Locally compact space, Group (periodic table), Compact space, Discrete mathematics, Pure mathematics, Combinatorics, Countable set, Physics, Mathematical physics, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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