| 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 compact type, 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. For CohFTs, Dunin-Barkowski, Orantin, Shadrin and Spitz have established a dictonary between (semisimple) CohFTs and topological recursion, building on Givental-Teleman symmetries. For F-CohFTs there is a similar dictionary with a non-symmetric version of topological recursion. This talk will be an introduction to F-CohFTs, their symmetries (F-Givental ones and a new one called "bridge") and the (so far partial) relations to non-symmetric topological recursion --- based on ongoing work with Alessandro Giacchetto and Giacomo Umer. |
