Geometry of mutation classes of rank 3 quivers

Felikson, A.; Tumarkin, P.

Abstract

We present a geometric realization for all mutation classes of quivers of rank 3 with real weights. This realization is via linear reflection groups for acyclic mutation classes and via groups generated by π-rotations for the cyclic ones. The geometric behavior of the model turns out to be controlled by the Markov constant p2 + q2 + r 2 − pqr, where p, q,r are the weights of arrows in a quiver. We also classify skew-symmetric mutation-finite real 3×3 matrices and explore the structure of acyclic representatives in finite and infinite mutation classes.

Citation

Felikson, A., & Tumarkin, P. (2019). Geometry of mutation classes of rank 3 quivers. Arnold Mathematical Journal, 5(1), 37-55. https://doi.org/10.1007/s40598-019-00101-2

• Journal Article Type: Article
• Acceptance Date: Feb 18, 2019
• Online Publication Date: Mar 4, 2019
• Publication Date: Mar 31, 2019
• Deposit Date: Oct 27, 2016
• Publicly Available Date: May 24, 2019
• Journal: Arnold Mathematical Journal
• Print ISSN: 2199-6792
• Electronic ISSN: 2199-6806
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 5
• Issue: 1
• Pages: 37-55
• DOI: https://doi.org/10.1007/s40598-019-00101-2
• Public URL: https://durham-repository.worktribe.com/output/1402135
• Related Public URLs: http://arxiv.org/abs/1609.08828