Wall-crossing structures in Donaldson-Thomas invariants, integrable systems and Mirror Symmetry

  title={Wall-crossing structures in Donaldson-Thomas invariants, integrable systems and Mirror Symmetry},
  author={Maxim Kontsevich and Yan S. Soibelman},
  journal={arXiv: Algebraic Geometry},
We introduce the notion of Wall-Crossing Structure and discuss it in several examples including complex integrable systems, Donaldson-Thomas invariants and Mirror Symmetry. For a big class of non-compact Calabi-Yau 3-folds we construct complex integrable systems of Hitchin type with the base given by the moduli space of deformations of those 3-folds. Then Donaldson-Thomas invariants of the Fukaya category of such a Calabi-Yau 3-fold can be (conjecturally) described in two more ways: in terms… 

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