Twisted Topological Graph Algebras

We define the notion of a twisted topological graph algebra associated to a topological graph and a $1$-cocycle on its edge set. We prove a stronger version of a Vasselli's result. We expand Katsura's results to study twisted topological graph algebras. We prove a version of the Cuntz-Krieger uniqueness theorem, describe the gauge-invariant ideal structure. We find that a twisted topological graph algebra is simple if and only if the corresponding untwisted one is simple.Comment: 27 page

Hamiltonian circle actions with minimal isolated fixed points

Let the circle act in a Hamiltonian fashion on a compact symplectic manifold $(M, \omega)$ of dimension $2n$. Then the $S^1$-action has at least $n+1$ fixed points. We study the case when the fixed point set consists of precisely $n+1$ isolated points. We show certain equivalence on the first Chern class of $M$ and some particular weight of the $S^1$-action at some fixed point. We show that the particular weight can completely determine the integral cohomology ring of $M$, the total Chern class of $M$, and the sets of weights of the $S^1$-action at all the fixed points. We will see that all these data are isomorphic to those of known examples, \CP^n, or \Gt_2(\R^{n+2}) with $n\geq 3$ odd, equipped with standard circle actions.Comment: title is slightly changed. Some contents are change

Extension of Spot Recovery Model for Gaussian Copula

Heightened systematic risk in the credit crisis has created challenges to CDO pricing and risk management. One important focus has been on the modeling of stochastic recovery. Different approaches within the Gaussian Copula framework have been proposed, but a consistent model was lacking until the recent paper of Bennani and Maetz [6] which shifted the modeling from period recovery to spot recovery. In this paper, we generalize their model to an arbitrary spot recovery distribution setup and extend the deterministic dependency on systematic factor to a random one. Besides, an extra parameter is introduced to control the correlation between default and recovery rate and the correlation between the recovery rates.CDO, Gaussian Copula, Stochastic Recovery, Spot Recovery Model

Twisted Topological Graph Algebras Are Twisted Groupoid C*-algebras

The second author showed how Katsura's construction of the C*-algebra of a topological graph E may be twisted by a Hermitian line bundle L over the edge space E. The correspondence defining the algebra is obtained as the completion of the compactly supported continuous sections of L. We prove that the resulting C*-algebra is isomorphic to a twisted groupoid C*-algebra where the underlying groupoid is the Renault-Deaconu groupoid of the topological graph with Yeend's boundary path space as its unit space.Comment: Revised version, to appear in J. Operator Theor