Mathematische Annalen

, Volume 358, Issue 1–2, pp 1–24 | Cite as

Principal graph stability and the jellyfish algorithm

  • Stephen Bigelow
  • David PenneysEmail author


We show that if the principal graph of a subfactor planar algebra of modulus \(\delta >2\) is stable for two depths, then it must end in \(A_{ finite }\) tails. This result is analogous to Popa’s theorem on principal graph stability. We use these theorems to show that an \(n-1\) supertransitive subfactor planar algebra has jellyfish generators at depth \(n\) if and only if its principal graph is a spoke graph. This is the published version of arxiv:1208.1564.

Mathematics Subject Classification (2000)

Primary 46L37 Secondary 18D05 57M20 



The authors would like to thank Vaughan Jones, Scott Morrison, and Sorin Popa for many helpful conversations. David Penneys was supported by NSF grant DMS-0856316 and DOD-DARPA grants HR0011-11-1-0001 and HR0011-12-1-0009.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.University of California, Santa BarbaraSanta BarbaraUSA
  2. 2.University of TorontoTorontoCanada

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