On pseudo-Anosov autoequivalences

Yu Wei Fan, Simion Filip, Fabian Haiden, Ludmil Katzarkov, Yijia Liu

Research output: Contribution to journalArticlepeer-review

Abstract

Motivated by results of Thurston, we prove that any autoequivalence of a triangulated category induces a filtration by triangulated subcategories, provided the existence of Bridgeland stability conditions. The filtration is given by the exponential growth rate of masses under iterates of the autoequivalence, and only depends on the choice of a connected component of the stability manifold. We then propose a new definition of pseudo-Anosov autoequivalences, and prove that our definition is more general than the one previously proposed by Dimitrov, Haiden, Katzarkov, and Kontsevich. We construct new examples of pseudo-Anosov autoequivalences on the derived categories of quintic Calabi–Yau threefolds and quiver Calabi–Yau categories. Finally, we prove that certain pseudo-Anosov autoequivalences on quiver 3-Calabi–Yau categories act hyperbolically on the space of Bridgeland stability conditions.

Original languageEnglish (US)
Article number107732
JournalAdvances in Mathematics
Volume384
DOIs
StatePublished - Jun 25 2021

Keywords

  • Autoequivalences
  • Bridgeland stability conditions
  • Pseudo-Anosov maps
  • Triangulated categories

ASJC Scopus subject areas

  • Mathematics(all)

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