Mathematische Zeitschrift

, Volume 292, Issue 1–2, pp 33–56 | Cite as

Cluster tilting subcategories and torsion pairs in Igusa–Todorov cluster categories of Dynkin type \(A_{ \infty }\)

  • Sira Gratz
  • Thorsten Holm
  • Peter JørgensenEmail author


We give a combinatorial classification of cluster tilting subcategories and torsion pairs in Igusa–Todorov cluster categories of Dynkin type \(A_{ \infty }\).


Cyclically ordered set Fountain Infinite polygon Leapfrog Ptolemy condition Ptolemy diagram Triangulation 

Mathematics Subject Classification

13F60 18E30 



We thank Charles Paquette, Adam-Christiaan van Roosmalen, and Bin Zhu for illuminating comments on a preliminary version, and the referee for a careful reading and several useful suggestions which have improved the presentation. This project was supported by grant HO 1880/5-1 under the research priority programme SPP 1388 “Darstellungstheorie” of the DFG, and by grant EP/P016014/1 “Higher Dimensional Homological Algebra” from the EPSRC.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of GlasgowGlasgowUK
  2. 2.Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Fakultät für Mathematik und PhysikLeibniz Universität HannoverHannoverGermany
  3. 3.School of Mathematics, Statistics and PhysicsNewcastle UniversityNewcastle upon TyneUK

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