A Non-crossing Word Cooperad for Free Homotopy Probability Theory

Part of the MATRIX Book Series book series (MXBS, volume 1)


We construct a cooperad which extends the framework of homotopy probability theory to free probability theory. The cooperad constructed, which seems related to the sequence and cactus operads, may be of independent interest.


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The author gratefully acknowledges useful conversations with Joey Hirsh, John Terilla, Jae-Suk Park, and Ben Ward. An anonymous referee made multiple useful observations.

This work was supported by IBS-R003-D1.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Geometry and PhysicsInstitute for Basic Science (IBS)PohangRepublic of Korea

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