Tropical intersection theory on R^n

TL;DR

This paper surveys tropical intersection theory on R^n, deriving properties of tropical cycles from Chow cohomology, and introduces a pull back operation that aligns with classical intersection theory principles.

Contribution

It introduces a pull back for tropical cycles based on Minkowski weights and connects tropical intersection theory with Chow cohomology, establishing key properties.

Findings

Defined a pull back for tropical cycles that commutes with intersection products.

Derived properties of tropical cycles from Chow cohomology.

Established the projection formula for tropical cycles.

Abstract

In these notes we survey the tropical intersection theory on R^n by deriving the properties for tropical cycles from the corresponding properties in Chow cohomology. For this we review the stable intersection product introduced by Mikhalkin and the push forward of tropical cycles defined by Allermann and Rau. Furthermore we define a pull back for tropical cycles based on the pull back of Minkowski weights. This pull back commutes with the tropical intersection product and satisfies the projection formula. Our main result is to deduce the latter from the corresponding projection formula in Chow cohomology.