5 research outputs found
Tropical eigenwave and intermediate Jacobians
Tropical manifolds are polyhedral complexes enhanced with certain kind of
affine structure. This structure manifests itself through a particular
cohomology class which we call the eigenwave of a tropical manifold. Other wave
classes of similar type are responsible for deformations of the tropical
structure.
If a tropical manifold is approximable by a 1-parametric family of complex
manifolds then the eigenwave records the monodromy of the family around the
tropical limit. With the help of tropical homology and the eigenwave we define
tropical intermediate Jacobians which can be viewed as tropical analogs of
classical intermediate Jacobians.Comment: 38 pages, 8 figure
Two dimensional periodic box-ball system and its fundamental cycle
We study a 2-dimensional Box-Ball system which is a ultradiscrete analog of
the discrete KP equation. We construct an algorithm to calculate the
fundamental cycle, which is an important conserved quantity of the 2-dim.
Box-Ball system with periodic boundary condition, by using the tropical curve
theory.Comment: 16 pages, 5 figure