English

On a Nielsen-Thurston classification theory for cluster modular groups

Geometric Topology 2018-06-01 v2 Quantum Algebra

Abstract

We classify elements of a cluster modular group into three types. We characterize them in terms of fixed point property of the action on the tropical compactifications associated with the corresponding cluster ensemble. The characterization gives an analogue of the Nielsen-Thurston classification theory on the mapping class group of a surface.

Keywords

Cite

@article{arxiv.1704.06586,
  title  = {On a Nielsen-Thurston classification theory for cluster modular groups},
  author = {Tsukasa Ishibashi},
  journal= {arXiv preprint arXiv:1704.06586},
  year   = {2018}
}

Comments

33 pages, 9 figures. To appear in Annales de l'Institut Fourier

R2 v1 2026-06-22T19:23:56.472Z