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In Jack Morava's paper On the complex cobordism ring as a Fock representation, it was remarked right at the beginning that complex cobordism may play a role in the theory of integrable systems. In another talk abstract by K. E. Feldman, it was mentioned that certain divisibility phenomena of Chern numbers are related to integrable systems. However the contents of the talks are nowhere to be found.

These are the only instances of the two topics in the title were mentioned to be related, that I managed to find after a brief search. My questions are: whether work or updates along these directions have been conducted since then. Or are there some general heuristics about how these topics might be related? Thanks.

Morava, Jack, On the complex cobordism ring as a Fock representation, Homotopy theory and related topics, Proc. Int. Conf., Kinosaki/Japan 1988, Lect. Notes Math. 1418, 184-204 (1990). ZBL0698.55003.

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  • $\begingroup$ Is it supposed to be related to classical or quantum integrability? $\endgroup$
    – Jules Lamers
    Commented Dec 22, 2023 at 22:17
  • $\begingroup$ In any case, integrable models are defined in two dimensions: either with a 2d space (in classical statistical mechanics, at thermal equilibrium so no time evolution) or in 1+1d: space + time (classical or quantum mechanics). Physically these manifold are real, but one often complexifies, so I can imagine that the 1+1d versions might be related to cobordisms $\endgroup$
    – Jules Lamers
    Commented Dec 22, 2023 at 22:23
  • $\begingroup$ Have you looked at the series of papers of Katsura, Shimizu and Ueno (and various more recent papers eg by Plaza Martin)? specifically "Complex cobordism ring and conformal field theory over Z" continues the direction in the Morava paper you cite. This is the same setting (the Fock space) as the KP hierarchy, tau functions etc. On the other hand, the Fock space or space of symmetric functions or of characteristic classes has so many structures and manifestations, and it's not clear one should take its appearance in two different areas as evidence of a strong connection between them. $\endgroup$
    – David Ben-Zvi
    Commented Dec 23, 2023 at 5:55

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