Cyclic posets and triangulation clusters
Triangulated categories coming from cyclic posets were originally introduced by the authors in a previous paper as a generalization of the constructions of various triangulated categories with cluster structures. We give an overview, and then analyze “triangulation clusters” which are those corresponding to topological triangulations of the 2-disk. Locally finite nontriangulation clusters give topological triangulations of the “cactus space” associated to the “cactus cyclic poset”.
Keywordscactus cyclic poset cluster structure triangulated categories Frobenius categories cocycle
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The authors thank Professors Bin Zhu, Fang Li and Zongzhu Lin for their hospitality at Tsinghua University and at the Chern Institute of Mathematics during the Workshop on Cluster Algebras and Related Topics, July 10–13, 2017. A series of lectures on this topic were given by the authors, which motivated the beginning of this paper and subsequent work for the rest of the paper.
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