Coloured quivers for rigid objects and partial triangulations: The unpunctured case
Representation Theory
2020-12-21 v4 Category Theory
Geometric Topology
Abstract
We associate a coloured quiver to a rigid object in a Hom-finite 2-Calabi--Yau triangulated category and to a partial triangulation on a marked (unpunctured) Riemann surface. We show that, in the case where the category is the generalised cluster category associated to a surface, the coloured quivers coincide. We also show that compatible notions of mutation can be defined and give an explicit description in the case of a disk. A partial description is given in the general 2-Calabi-Yau case. We show further that Iyama-Yoshino reduction can be interpreted as cutting along an arc in the surface.
Cite
@article{arxiv.1012.5790,
title = {Coloured quivers for rigid objects and partial triangulations: The unpunctured case},
author = {Bethany Marsh and Yann Palu},
journal= {arXiv preprint arXiv:1012.5790},
year = {2020}
}
Comments
29 pages, 17 figures. Discussion in Section 6 clarified and expanded. Some minor corrections, clarification of notation