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Blobbed topological recursion and KP integrability

Selecta Mathematica, New Series. 2026. Vol. 32. Article 25.
Alexandrov A., Bychkov B., Dunin-Barkowski P., Kazaryan M., Shadrin S.

We revise the notion of the blobbed topological recursion by extending it to the setting of generalized topological recursion as well as allowing blobs which do not necessarily admit topological expansion. We show that the so-called non-perturbative differentials form a special case of this revisited version of blobbed topological recursion. Furthermore, we prove the KP integrability of the differentials of blobbed topological recursion for the input data that include KP-integrable blobs. This result generalizes, unifies, and gives a new proof of the KP integrability of nonperturbative differentials conjectured by Borot–Eynard and recently proved by the authors.

Research target: Mathematics
Language: English
Full text
DOI
Keywords: topological recursion KP integrabilityBlobs KP integrabile hierarchy
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