Cyclic posets and triangulation clusters

  • Kiyoshi Igusa
  • Gordana TodorovEmail author
Articles Special Topic on Cluster Algebras


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”.


cactus cyclic poset cluster structure triangulated categories Frobenius categories cocycle 


18E30 16G20 


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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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© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsBrandeis UniversityWalthamUSA
  2. 2.Department of MathematicsNortheastern UniversityBostonUSA

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