MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Are there any good short expositions of planar algebras out there? I am interested primarily in seeing the main definition and some explicit examples.

share|cite|improve this question
up vote 9 down vote accepted

My paper with Emily and Noah about the D_{2n} planar algebra includes our attempt at a friendly explanation. It's all about arguably the simplest non-trivial example of a subfactor planar algebra.

share|cite|improve this answer
This looks great. Thanks! – Elisha Peterson Oct 17 '09 at 16:01

Emily and Noah wrote some really nice expository posts on planar algebras at the Secret Blogging Seminar. I also like Chris's posts on TQFTs and Planar Algebras to explain why I might care.

share|cite|improve this answer

Vaughan Jones' paper "The planar algebra of a bipartite graph" is short and example-focused. It's got the "right" definition (phrased with operads) and the mechanics of the bipartite graph planar algebra. While the bipartite graph planar algebra isn't a subfactor planar algebra, it's pretty darn close.

A subfactor planar algebra, by the way, is one which meets restrictions on the sizes of the spaces involved and has an inner product. Unsurprisingly, they give rise to subfactors (through machinery of Popa).

share|cite|improve this answer

Vijay Kodiyalam gave a series of polished lectures introducing to the planar algebras theory, the videos (HD) are available in the following link: Vijay Kodiyalam - Planar algebras - IMSc 2015
By watching the first lectures, you will quickly get a good understanding of the definition and examples.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.