A conjectural formula for $DR_g(a,-a) \lambda_g$

TL;DR

The paper proposes a conjectural formula for a specific geometric class involving double ramification cycles and lambda classes, verifies its properties, and shows its equivalence to a previous conjecture.

Contribution

It introduces a new conjectural formula for $DR_g(a,-a) \lambda_g$, refining previous work and establishing its equivalence to earlier conjectures.

Findings

The proposed formula satisfies all expected properties.

The conjecture is shown to be equivalent to a prior conjecture.

The work advances understanding of double ramification cycles.

Abstract

We propose a conjectural formula for $DR_g(a,-a) \lambda_g$ and check all its expected properties. Our formula refines the one point case of a similar conjecture made by the first named author in collaboration with Gu\'er\'e and Rossi, and we prove that the two conjectures are in fact equivalent, though in a quite non-trivial way.