Year: 2012
Type: preprint
Abstract: We construct universal geometric coefficients, over the integers, the rationals, and the reals, for cluster algebras arising from the once-punctured torus. We verify that the once-punctured torus has a property called the Null Tangle Property. The universal geometric coefficients over the integers and the rationals are then given by the shear coordinates of certain "allowable" curves in the torus. The universal geometric coefficients over the reals are given by the shear coordinates of allowable curves together with the normalized shear coordinates of certain other curves each of which is dense in the torus. We also construct the mutation fan for the once-punctured torus and recover a result of Nájera on g-vectors.
Source: arXiv (Cornell University)
Author: Reading, Nathan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2128767097