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Duality for toric Landau-Ginzburg models. (English) Zbl 1386.81130
In the publication the author generalises the mirror symmetry of pairs of Calabi-Yau manifolds to Kähler manifolds for which he uses a Landau-Ginzburg model as a mean to express this mirror symmetry. This Landau-Ginzburg model is imported to topology from the theory of superconductivity. Therefore, from the first sight on the title the reader might think that the publication deals with superconductivity. Only the adjective “toric” provides a first caveat. Actually, the subject is symplectic topology. In scanning the literature dealing with Landau-Ginzburg models in topology gives no hint on how this model is related to the treatment in superconductivity.
For a reader not being accustomed to the terms of symplectic topology (like me), the barrage of technical terms is frightening and keeps from reading this publication. The author uses the slang of his area of expertise which makes understanding quite difficult. For instance, he speaks of “Calabi-Yau” instead of “Calabi-Yau manifold” and “Gorenstein” as an adjective. Except for the general statement that a model can help to generalise a symmetry, the publication is not suitable for a broader audience. The expert in this field might get some deeper insight into articular considerations. However, the reader from outside with interest in topology will have difficulties to read this publication.

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T60 Supersymmetric field theories in quantum mechanics
14J33 Mirror symmetry (algebro-geometric aspects)
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
32Q15 Kähler manifolds
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