1. CJM Online first
 Allermann, Lars; Hampe, Simon; Rau, Johannes

On rational equivalence in tropical geometry
This article discusses the concept of rational equivalence
in tropical
geometry
(and replaces an older and imperfect version).
We give the basic definitions in the context of tropical varieties
without boundary points and prove some basic properties.
We then compute the ``bounded'' Chow groups of $\mathbb{R}^n$ by showing
that they are isomorphic
to the group of fan cycles. The main step in the proof is of
independent interest:
We show that every tropical cycle in $\mathbb{R}^n$ is a sum of (translated)
fan cycles. This also
proves that the intersection ring of tropical cycles is generated
in codimension 1 (by hypersurfaces).
Keywords:tropical geometry, rational equivalence Category:14T05 

2. CJM 2014 (vol 67 pp. 527)
 Brugallé, Erwan; Shaw, Kristin

Obstructions to Approximating Tropical Curves in Surfaces Via Intersection Theory
We provide some new local obstructions to
approximating
tropical curves in
smooth tropical surfaces. These obstructions are based on
a
relation between tropical and complex intersection theories which is
also established here. We give
two applications of the methods developed in this paper.
First we classify all locally irreducible approximable 3valent fan tropical
curves in a
fan tropical plane.
Secondly, we prove that a generic nonsingular
tropical surface
in tropical projective 3space contains finitely
many approximable tropical lines
if
it is of degree 3, and contains no approximable tropical lines if
it is of degree 4 or more.
Keywords:tropical geometry, amoebas, approximation of tropical varieties, intersection theory Categories:14T05, 14M25 

3. CJM 2012 (vol 65 pp. 120)
 Francois, Georges; Hampe, Simon

Universal Families of Rational Tropical Curves
We introduce the notion of families of $n$marked
smooth rational tropical curves over smooth tropical varieties and
establish a onetoone correspondence between (equivalence classes of)
these families and morphisms
from smooth tropical varieties into the moduli space of $n$marked
abstract rational tropical curves $\mathcal{M}_{n}$.
Keywords:tropical geometry, universal family, rational curves, moduli space Categories:14T05, 14D22 

4. CJM 2011 (vol 64 pp. 845)
 Helm, David; Katz, Eric

Monodromy Filtrations and the Topology of Tropical Varieties
We study the topology of tropical varieties that arise from a certain
natural class of varieties. We use the theory of tropical
degenerations to construct a natural, ``multiplicityfree''
parameterization of $\operatorname{Trop}(X)$ by a topological space
$\Gamma_X$ and give a geometric interpretation of the cohomology of
$\Gamma_X$ in terms of the action of a monodromy operator on the
cohomology of $X$. This gives bounds on the Betti numbers of
$\Gamma_X$ in terms of the Betti numbers of $X$ which constrain the
topology of $\operatorname{Trop}(X)$. We also obtain a description of
the top power of the monodromy operator acting on middle cohomology of
$X$ in terms of the volume pairing on $\Gamma_X$.
Categories:14T05, 14D06 
