Finitely presented left orderable monsters
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Date
2024-05
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Journal Article
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Abstract
A left orderable monster is a finitely generated left orderable group all of whose fixed point-free actions on the line are proximal: the action is semiconjugate to a minimal action so that for every bounded interval I and open interval J, there is a group element that sends I into J. In his 2018 ICM address, Navas asked about the existence of left orderable monsters. By now there are several examples, all of which are finitely generated but not finitely presentable. We provide the first examples of left orderable monsters that are finitely presentable, and even of type Fâ. These groups satisfy several additional properties separating them from the previous examples: they are not simple, they act minimally on the circle, and they have an infinite-dimensional space of homogeneous quasimorphisms. Our construction is flexible enough that it produces infinitely many isomorphism classes of finitely presented (and type Fâ) left orderable monsters.
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published
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Volume
44 (5)
Pages / Article No.
1367 - 1378
Publisher
Cambridge University Press
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Subject
left orderable group; action on the line; action on the circle; rotation number; finiteness properties
Organisational unit
08802 - Iozzi, Alessandra (Tit.-Prof.)
02000 - Dep. Mathematik / Dep. of Mathematics
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