Cohomology of quiver moduli, functional equations, and integrality of Donaldson-Thomas type invariants

Abstract

A system of functional equations relating the Euler characteristics of moduli spaces of stable representations of quivers and the Euler characteristics of (Hilbert scheme-type) framed versions of quiver moduli is derived. This is applied to wall-crossing formulas for the Donaldson-Thomas type invariants of M. Kontsevich and Y. Soibelman, in particular confirming their integrality.

24 pages

References in corpus (6)

• The tropical vertex
• Moduli of representations of quivers
• Cohomology of non-commutative Hilbert schemes
• Poisson automorphisms and quiver moduli
• Smooth models of quiver moduli
• Mahler Measure Variations, Eisenstein Series and Instanton Expansions

Cited by in corpus (38)

• Quantum Wall Crossing in N=2 Gauge Theories
• Riemann-Hilbert problems from Donaldson-Thomas theory
• Wild Wall Crossing and BPS Giants
• BPS states, knots and quivers
• Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants
• Spectral Networks with Spin
• The quantum tropical vertex
• Topological strings, strips and quivers
• Donaldson-Thomas invariants, torus knots, and lattice paths
• Quiver mutation and combinatorial DT-invariants
• Donaldson-Thomas theory for categories of homological dimension one with potential
• BPS counting for knots and combinatorics on words
• BPS Hall Algebra of Scattering Hall States
• Aspects of the topology and combinatorics of Higgs bundle moduli spaces
• On higher rank Donaldson-Thomas invariants
• Regge Trajectories in $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory
• Abelian quiver invariants and marginal wall-crossing
• A proof of N.Takahashi's conjecture for $({\mathbb{P}}^2,E)$ and a refined sheaves/Gromov-Witten correspondence
• Strong positivity for quantum theta bases of quantum cluster algebras
• Counting Trees in Supersymmetric Quantum Mechanics
• Donaldson-Thomas invariants vs. intersection cohomology for categories of homological dimension one
• Asymptotics of Ground State Degeneracies in Quiver Quantum Mechanics
• Nahm sums, quiver A-polynomials and topological recursion
• A refinement of the A-polynomial of quivers
• Quiver diagonalization and open BPS states
• Log BPS numbers of log Calabi-Yau surfaces
• Algebraicity and Asymptotics: An explosion of BPS indices from algebraic generating series
• Floer theory of higher rank quiver 3-folds
• Quivers and curves in higher dimension
• Combinatorics of Nahm sums, quiver resultants and the K-theoretic condition
• Quivers, curves, and the tropical vertex
• An introduction into (motivic) Donaldson-Thomas theory
• D0-D6 states counting and GW invariants
• Explicit forms in lower degrees of rank 2 cluster scattering diagrams
• Quantum dilogarithms and partition q-series
• On an example of quiver DT/relative GW correspondence
• Chern-Simons functions on toric Calabi-Yau threefolds and Donaldson-Thomas theory
• Refined GW/Kronecker correspondence