Dehornoy-like left orderings and isolated left orderings

Abstract

We introduce a Dehornoy-like ordering of groups, which is a generalization of the Dehornoy ordering of the braid groups. Under a weak assumption which we call Property F, we show that Dehornoy-like orderings have properties similar to the Dehornoy ordering, and produce isolated left orderings. We also construct new examples of Dehornoy-like ordering and isolated orderings and study their more precise properties.

17 pages, 2 figures

References in corpus (4)

• The space of left orders of a group is either finite or uncountable
• Braid ordering and the geometry of closed braid
• A new characterization of Conrad's property for group orderings, with applications
• Construction of isolated left orderings via partially central cyclic amalgamation

Cited by in corpus (4)

• Orderings and flexibility of some subgroups of $Home{o}_{+}(\mathbb{R})$
• Construction of isolated left orderings via partially central cyclic amalgamation
• Dense orderings in the space of left-orderings of a group
• Spaces of orders of some one-relator groups