Tropical (1,1)-homology for floor decomposed surfaces
Kristin Shaw · Contemporary mathematics - American Mathematical Society · 2013
The tropical ( p , q ) (p, q) -homology groups of Itenberg, Katzarkov, Mikhalkin and Zharkov (preprint) are the tropical analogues of the Hodge decomposition of the cohomology of complex algebraic varieties. Following ideas of Mikhalkin, in Shaw ( Tropical intersection theory and surfaces ) it is shown that there is a well-defined intersection pairing on tropical ( 1 , 1 ) (1, 1) -classes of a compact non-singular tropical surface. Here we compute directly the ( 1 , 1 ) (1, 1) -homology of a non-singular floor decomposed tropical surface in tropical projective space, along with the intersection form.