XXXVI Workshop on Geometric Methods in Physics | 2-8.07.2017 |

VI School on Geometry and Physics | 26-30.06.2017 |

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## Mirela Babalic## A differential model for B-type Landau-Ginzburg theoriesWe describe a mathematically rigorous differential model for B-type open-closed topological Landau-Ginzburg theories defined by a pair (X,W), where X is a non-compact Kahlerian manifold with holomorphically trivial canonical line bundle and W is a complex-valued holomorphic function defined on X and whose critical locus is compact but need not consist of isolated points. In this generality, we give rigorous constructions of the topological D-brane category, bulk algebra, bulk-boundary and boundary-bulk maps as well as of the bulk and boundary topological traces. We also show how this construction specializes to the case when X is Stein and W has finite critical set, in which case one recovers a simpler mathematical model. |

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