The eta invariant of the Dirac operator over a noncompact cofinite quotient of PSL(2,R) is defined through a regularized trace following Melrose. It reduces to the standard definition in terms of eigenvalues in the case of a totally nontrivial spin structure. When the S1-fibers are rescaled, the metric becomes of nonexact fibred-cusp type near the ends. We completely describe the continuous spe...

We extend the notion of exact completion on a category with weak finite limits to Lawvere’s elementary doctrines. We show how any such doctrine admits an elementary quotient completion, which is the universal solution to adding certain quotients. We note that the elementary quotient completion can be obtained as the composite of two other universal constructions: one adds effective quotients, t...

A duality transform for the coalgebra of the free difference quotient derivationmultiplication of an operator with respect to a free algebra of scalars is constructed. The dual object is realized in an algebra of matricial analytic functions endowed with yet another generalization of the difference quotient derivation.

This paper studies the canonical Chow quotient of a smooth projective variety by a reductive algebraic group. The main observation of this paper is that, over the field of complex numbers, the Chow quotient admits symplectic and other topological interpretations, namely, symplectically, the moduli spaces of stable orbits with prescribed momentum charges; and topologically, the moduli space of s...

In humans, oxytocin (OT) enhances prosocial behaviour. However, it is still unclear how the prosocial effects of OT are modulated by emotional features and/or individuals' characteristics. In a placebo-controlled design, we tested 20 healthy male volunteers to investigate these behavioural and neurophysiological modulations using magnetoencephalography. As an index of the individuals' character...

This article is motivated by the following local-to-global question: is every variety with tame quotient singularities globally the quotient of a smooth variety by a finite group? We show that this question has a positive answer for all quasi-projective varieties which are expressible as a quotient of a smooth variety by a split torus (e.g. simplicial toric varieties). Although simplicial toric...

We classify those manifolds mentioned in the title which have finite topological type. Namely we show any such connected M is isomorphic to a hyperkähler quotient of a flat quaternionic vector space H by an abelian group. We also show that a compact connected and simply connected 3-Sasakian manifold of dimension 4n− 1 whose isometry group has rank n+1 is isometric to a 3-Sasakian quotient of a ...

In this note we observe that, contrary to the usual lore, string orbifolds do not describe strings on quotient spaces, but rather seem to describe strings on objects called quotient stacks, a result that follows from simply unraveling definitions, and is further justified by a number of results. Quotient stacks are very closely related to quotient spaces; for example, when the orbifold group ac...

OBJECTIVE To investigate the characteristics of attention in school-age children with mild autism spectrum disorder (ASD), and to provide a basis for clinical treatment. METHODS A total of 20 school-age children with mild ASD were enrolled, and the intermediate visual and auditory continuous performance test (IVA-CPT) was used to assess their attention. A total of 20 children with attention d...