| Résume | F-CohFTs are collections of cohomology classes on the moduli space of curves compatible with pinching separating cycles, unlike CohFTs which are compatible with pinching any kind of cycles. F-CohFTs appear naturally when looking at the moduli space of complex curves with compact Jacobian, and by work of Buryak and Rossi they can be used in combination with the geometry of the double ramification cycle to produce integrable hierarchies. Since there are less constraints, the world of F-CohFT is richer that those of CohFTs. I will describe a group of symmetries of F-CohFTs which enlarge the known F-Givental group of Arsie-Buryak-Rossi-Lorenzoni by a large set of linear symmetries. For CohFTs, Dunin-Barkowski, Orantin, Shadrin and Spitz have established a dictonary between (semisimple) CohFTs and topological recursion, building on Givental symmetries and Teleman reconstruction. I will describe the analogue of this dictionary in the F-world (though it is less powerful in absence of Teleman's reconstruction). This is based on a work soon to appear with Alessandro Giacchetto and Giacomo Umer. |
