The pure cohomology of multiplicative quiver varieties

To a quiver Q and choices of nonzero scalars $$q_i$$ q i , non-negative integers $$\alpha _i$$ α i , and integers $$\theta _i$$ θ i labeling each vertex i, Crawley-Boevey–Shaw associate a multiplicative quiver variety$${\mathcal {M}}_\theta ^q(\alpha )$$ M θ q ( α ) , a trigonometric analogue of the Nakajima quiver variety associated to Q, $$\alpha $$ α , and $$\theta $$ θ . We prove that the pure cohomology, in the Hodge-theoretic sense, of the stable locus $${\mathcal {M}}_\theta ^q(\alpha )^{{\text {s}}}$$ M θ q ( α ) s is generated as a $${\mathbb {Q}}$$ Q -algebra by the tautological characteristic classes. In particular, the pure cohomology of genus g twisted character varieties of $$GL_n$$ G L n is generated by tautological classes.

Donaldson–Thomas invariants versus intersection cohomology of quiver moduli

The main result of this paper is the statement that the Hodge theoretic Donaldson–Thomas invariant for a quiver with zero potential and a generic stability condition agrees with the compactly supported intersection cohomology of the closure of the stable locus inside the associated coarse moduli space of semistable quiver representations. In fact, we prove an even stronger result relating the Donaldson–Thomas “function” to the intersection complex. The proof of our main result relies on a relative version of the integrality conjecture in Donaldson–Thomas theory. This will be the topic of the second part of the paper, where the relative integrality conjecture will be proven in the motivic context.

Locus of Control and Biofeedback: A Review of the Literature

This paper first reviews studies which have investigated the efficacy of using locus of control orientation to predict performance in various modes of biofeedback. However, contradictory evidence and methodological problems make it impossible to draw any conclusions regarding the connection between internality-externality and biofeedback performance. Second, various attempts to modify externality through biofeedback treatment are reviewed. Although EMG feedback can apparently be used to shift locus of control in an internal direction, there are some major issues that need to be resolved. Of primary importance is the fact that the rationale for modifying externality is based on an unproven assumption that externality has a role in the causation of various undesirable behaviors. Also, as no follow-up testing has been done, there is no evidence that the EMG biofeedback causes relatively permanent, stable locus of control changes. If the shifts are only temporary, then its use as a modifier of externality is questionable.