Refined count of plane tropical curves of positive genus
We define refined tropical enumerative invariants counting plane tropical curves of a given degree and a given positive genus and having marked points on edges and at vertices. This extends Block-Goettsche and Goettsche-Schroeter refined tropical invariants. As a consequence we obtain tropical (complex) descendant invariants and (real) broccoli invariants of positive genus.
(Joint work with F. Schroeter.)