viewpoint*. Each of our admissible Dynkin subquiver partitions corresponds to a stability condition from the representation theory viewpoint. In this sense, our Theorem \[thm:main\] is implicit in the work of Franzen–Reineke and Davison–Meinhardt.

Thus, the major accomplishment of our paper is an *explicit topological realization, in the language of characteristic classes, of the isomorphism of Equation* . It would be interesting to consider if there exists stability conditions for which each factor ${\mathscr{H}}^{\theta-\mathrm{sst},\mu}$ is isomorphic to ${\mathscr{H}}(A_1)$, but which can not be realized topologically by an admissible Dynkin subquiver partition.

The structure of the paper is as follows. In Section \[s:quivers\] we lay out notations, definitions, and relevant preliminary results related to quivers and the equivariant cohomology algebras ${\mathscr{H}}_\gamma$. In Section \[s:coha\] we recall the definition of the CoHA and describe the $*$-multiplication explicitly. In Section \[s:imp.vars\] we describe several important varieties which are parameterized by combinatorial data associated to the quiver, and prove several results about their structure and relevance to the present setting. In Section \[s:q.dilog.poincare\] we recall results regarding quantum dilogarithm identities from [@ja2018] and describe their interpretation as Poincaré series for the CoHA. Our main results appear in Section \[s:structure\] and we complete the proof of 