Interpolating factorizations for acyclic Donaldson--Thomas invariants

TL;DR

This paper introduces a new family of factorization formulas for combinatorial Donaldson--Thomas invariants of acyclic quivers, extending known identities and providing explicit dimension counting methods.

Contribution

It develops interpolating factorization formulas for acyclic Donaldson--Thomas invariants, generalizing previous quantum dilogarithm identities and employing stratifications and Betti number calculations.

Findings

Established explicit factorization formulas for acyclic quivers.

Connected new formulas with existing quantum dilogarithm identities.

Used stratifications and equivariant cohomology to compute invariants.

Abstract

We prove a family of factorization formulas for the combinatorial Donaldson--Thomas invariant for an acyclic quiver. A quantum dilogarithm identity due to Reineke, later interpreted by Rimanyi by counting codimensions of quiver loci, gives two extremal cases of our formulation in the Dynkin case. We establish our interpolating factorizations explicitly with a dimension counting argument by defining certain stratifications of the space of representations for the quiver and calculating Betti numbers in the corresponding equivariant cohomology algebras.