Tropical geometry can be seen as an algebraic geometry based on tropical numbers.
The role of algebraic varieties in tropical geometry is played by certain piecewiselinear
objects,
called tropical varieties. Under some assumptions, a tropical variety can be approximated
by a oneparametric family of complex varieties, which provides an important link
between complex and tropical geometries.
The purpose of this talk is to discuss tropical homology together with its relations to Hodge
decompositions (respectively, homology)
in complex (respectively, real) world.
