Reconstruction of F-cohomological field theories on moduli of compact type

TL;DR

This paper extends Givental-Teleman reconstruction to F-cohomological field theories on the moduli space of compact type, enabling new relations between $$-classes.

Contribution

It develops an analogue of Givental-Teleman reconstruction for F-cohomological field theories on the moduli space of compact type.

Findings

Reconstructed extended $r$-spin classes on the moduli space.

Derived relations between $$-classes in compact type.

Applied the reconstruction to specific classes on the moduli space.

Abstract

We prove an analogue of Givental-Teleman reconstruction for F-cohomological field theories on the moduli space of compact type. We apply it to reconstruct the restriction of the extended $r$-spin classes to the extended direction and deduce relations between $\kappa$-classes (both in compact type).