Year: 2023
Type: article
Abstract: We recover the Dehornoy order on the braid group [Formula: see text] from the tracial state on a cluster [Formula: see text]-algebra [Formula: see text] associated to the surface [Formula: see text] of genus [Formula: see text] with [Formula: see text] boundary components. It is proved that the space of left-ordering of the fundamental group [Formula: see text] is a totally disconnected dense subspace of the projective Teichmüller space [Formula: see text]. In particular, each left-ordering of [Formula: see text] defines the orbit of a Riemann surface [Formula: see text] under the geodesic flow on the space [Formula: see text].
Source: Journal of Topology and Analysis
Author: Igor V. Nikolaev
Institution: St. John's University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4388638568