Cyclic posets and triangulation clusters

Abstract

Triangulated categories coming from cyclic posets were originally introduced by the authors in [IT15b] as a generalization of the constructions of various triangulated categories with cluster structures. We give an overview, then analyze triangulation clusters which are those corresponding to topological triangulations of the 2-disk. Locally finite non-triangulation clusters give topological triangulations of the cactus space associated to the cactus cyclic poset.

32 pages, 10 figures, presented by second author at Tsinghua University and at the Chern Institute of Mathematics, Nankai University, China, July 3-13, 2017, accepted for publication in SCIENCE CHINA Mathematics. v2: minor corrections, theorems renumbers

References in corpus (3)

• On Generalized Cluster Categories
• Cluster tilting vs. weak cluster tilting in Dynkin type A infinity
• $c$-vectors of 2-Calabi--Yau categories and Borel subalgebras of ${\mathfrak{sl}}_{\infty }$