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Infinite rank surface cluster algebras

Canakci, I.; Felikson, A.

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Authors

I. Canakci



Abstract

We generalise surface cluster algebras to the case of infinite surfaces where the surface contains finitely many accumulation points of boundary marked points. To connect different triangulations of an infinite surface, we consider infinite mutation sequences. We show transitivity of infinite mutation sequences on triangulations of an infinite surface and examine different types of mutation sequences. Moreover, we use a hyperbolic structure on an infinite surface to extend the notion of surface cluster algebras to infinite rank by giving cluster variables as lambda lengths of arcs. Furthermore, we study the structural properties of infinite rank surface cluster algebras in combinatorial terms, namely we extend “snake graph combinatorics” to give an expansion formula for cluster variables. We also show skein relations for infinite rank surface cluster algebras.

Journal Article Type Article
Acceptance Date May 21, 2019
Online Publication Date Jun 26, 2019
Publication Date Aug 20, 2019
Deposit Date Jun 3, 2019
Publicly Available Date Jun 26, 2020
Journal Advances in Mathematics
Print ISSN 0001-8708
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 352
Pages 862-942
DOI https://doi.org/10.1016/j.aim.2019.06.008
Public URL https://durham-repository.worktribe.com/output/1295330
Related Public URLs https://arxiv.org/abs/1704.01826

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