Tropological sigma models on 4D targets are defined on filtered manifolds with nilpotent Engel algebra symmetries and conjectured to correspond to filtered Gromov-Witten invariants.
Hyperfields for Tropical Geometry I. Hyperfields and dequantization
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abstract
New hyperfields, that is fields in which addition is multivalued, are introduced and studied. In a separate paper these hyperfields are shown to provide a base for the tropical geometry. The main hyperfields considered here are classical number sets, such as the set of complex numbers, the set of real numbers, and the set of real non-negative numbers, with the usual multiplications, but new, multivalued additions. The new hyperfields are related with the classical fields and each other by dequantisations. For example, the new complex tropical field is a dequantization of the field of complex numbers.
fields
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Nil-Equivariant Tropological Sigma Models on Filtered Geometries
Tropological sigma models on 4D targets are defined on filtered manifolds with nilpotent Engel algebra symmetries and conjectured to correspond to filtered Gromov-Witten invariants.