K-theoretic Gromov–Witten invariants in genus 0 and integrable hierarchies



We prove that the genus 0 invariants in K-theoretic Gromov–Witten theory are governed by an integrable hierarchy of hydrodynamic type. If the K-theoretic quantum product is semisimple, then we also prove the completeness of the hierarchy.


Frobenius structures K-theoretic Gromov–Witten invariants Integrable systems 

Mathematics Subject Classification

14N35 35Q53 



We are thankful to Y. Zhang for showing interest in our work and for several useful discussions. We also thank the anonymous referee for several useful suggestions as well as pointing out the relevance to our work of reference [4]. The work of T. M. is partially supported by JSPS Grant-In-Aid 2680003, JSPS Grant-in-Aid Kiban C 17K05193, and by the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. This work started during a visit of the second author to Kavli IPMU. V. T. would like to thank the institute for hospitality and support.


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Authors and Affiliations

  1. 1.Kavli IPMU (WPI), UTIASThe University of TokyoKashiwaJapan
  2. 2.Humboldt UniveritätBerlinGermany

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