Analytic and topological index maps with values in the K-theory of mapping cones

Index maps taking values in the $K$-theory of a mapping cone are defined and discussed. The resulting index theorem can be viewed in analogy with the Freed-Melrose index theorem. The framework of geometric $K$-homology is used in a fundamental way. In particular, an explicit isomorphism from a geometric model for $K$-homology with coefficients in a mapping cone, $C_{\phi}$, to $KK(C(X),C_{\phi})$ is constructed.Comment: 22 page

Relative geometric assembly and mapping cones, Part I: The geometric model and applications

Inspired by an analytic construction of Chang, Weinberger and Yu, we define an assembly map in relative geometric $K$-homology. The properties of the geometric assembly map are studied using a variety of index theoretic tools (e.g., the localized index and higher Atiyah-Patodi-Singer index theory). As an application we obtain a vanishing result in the context of manifolds with boundary and positive scalar curvature; this result is also inspired and connected to work of Chang, Weinberger and Yu. Furthermore, we use results of Wahl to show that rational injectivity of the relative assembly map implies homotopy invariance of the relative higher signatures of a manifold with boundary.Comment: 37 pages. Accepted in Journal of Topolog

The Canadian Debt-Strategy Model: An Overview of the Principal Elements

As part of managing a debt portfolio, debt managers face the challenging task of choosing a strategy that minimizes the cost of debt, subject to limitations on risk. The Bank of Canada provides debt-management analysis and advice to the Government of Canada to assist in this task, with the Canadian debt-strategy model being developed to help in this regard. The authors outline the main elements of the model, which include: cost and risk measures, inflation-linked debt, optimization techniques, the framework used to model the government’s funding requirement, the sensitivity of results to the choice of joint stochastic macroeconomic term-structure model, the effects of shocks to macroeconomic and term-structure variables and changes to their long-term values, and the relationship between issuance yield and issuance amount. Emphasis is placed on the degree to which changes to the formulation of model elements impact key results. The model is an important part of the decision-making process for the determination of the government’s debt strategy. However, it remains one of many tools that are available to debt managers and is to be used in conjunction with the judgment of an experienced debt manager.Debt management; Econometric and statistical methods; Financial markets; Fiscal policy

The bordism group of unbounded KK-cycles

We consider Hilsum's notion of bordism as an equivalence relation on unbounded $KK$-cycles and study the equivalence classes. Upon fixing two $C^*$-algebras, and a $*$-subalgebra dense in the first $C^*$-algebra, a $\mathbb{Z}/2\mathbb{Z}$-graded abelian group is obtained; it maps to the Kasparov $KK$-group of the two $C^*$-algebras via the bounded transform. We study properties of this map both in general and in specific examples. In particular, it is an isomorphism if the first $C^*$-algebra is the complex numbers (i.e., for $K$-theory) and is a split surjection if the first $C^*$-algebra is the continuous functions on a compact manifold with boundary when one uses the Lipschitz functions as the dense $*$-subalgebra.Comment: 38 page

Achieving accurate FTIR measurements on high performance bandpass filters

The sources of ordinate error in FTIR spectrometers are reviewed with reference to measuring small out-of-band features in the spectra of bandpass filters. Procedures for identifying instrumental artefacts are described. It is shown that features well below 0.01%T can be measured reliably

Realizing the analytic surgery group of Higson and Roe geometrically, Part II: Relative eta-invariants

We apply the geometric analog of the analytic surgery group of Higson and Roe to the relative $\eta$-invariant. In particular, by solving a Baum-Douglas type index problem, we give a "geometric" proof of a result of Keswani regarding the homotopy invariance of relative $\eta$-invariants. The starting point for this work is our previous constructions in "Realizing the analytic surgery group of Higson and Roe geometrically, Part I: The geometric model" (arXiv:1308.5990).Comment: 38 pages, to appear in Mathematische Annale