Related papers: On the rho invariant for manifolds with boundary
This is a survey of recent results on zeta- and eta-function poles and values for realizations of Laplace- and Dirac-type operators defined by pseudodifferential projection boundary conditions (including the Atiyah-Patodi-Singer operator…
On complete non-compact manifolds with bounded sectional curvature, we consider a class of self-adjoint Dirac-type operators called Dirac-Schr\"odinger operators. Assuming two Dirac-Schr\"odinger operators coincide at infinity, by previous…
We study realizations of pseudodifferential operators acting on sections of vector-bundles on a smooth, compact manifold with boundary, subject to conditions of Atiyah-Patodi-Singer type. Ellipticity and Fredholm property, compositions,…
We consider a family of boundary integral operators supported on a collection of parametrically defined bounded Lipschitz boundaries. Consequently, the boundary integral operators themselves also depend on the parametric variables, thus…
We study eta-invariants on odd dimensional manifolds with boundary. The dependence on boundary conditions is best summarized by viewing the (exponentiated) eta-invariant as an element of the (inverse) determinant line of the boundary. We…
We describe a relation between Atiyah-Patodi-Singer boundary condition and a global elliptic boundary condition which naturally appears in formulating a splitting formula for a spectral flow, when we decompose the manifold into two…
In this paper, an equality between the Hochs-Mathai type index and the Atiyah-Patodi-Singer type index is established when the manifold and the group action are both non-compact, which generalizes a result of Ma and Zhang for compact group…
This article surveys the relations among local and nonlocal invariants in Atiyah-Singer index theory. We discuss the local invariants that arise from the heat equation approach to the index theorem for geometric operators, as well as the…
We extend the Atiyah, Patodi, and Singer index theorem for first order differential operators from the context of manifolds with cylindrical ends to manifolds with periodic ends. This theorem provides a natural complement to Taubes'…
The construction of invariants of three-dimensional manifolds with a triangulated boundary, proposed earlier by the author for the case when the boundary consists of not more than one connected component, is generalized to any number of…
In this paper, we introduce several new secondary invariants for Dirac operators on a complete Riemannian manifold with a uniform positive scalar curvature metric outside a compact set and use these secondary invariants to establish a…
The {\em abstract boundary\/} (or {\em {\em a\/}-boundary\/}) of Scott and Szekeres \cite{Scott94} constitutes a ``boundary'' to any $n$-dimensional, paracompact, connected, Hausdorff, $C^\infty$-manifold (without a boundary in the usual…
Using adiabatic limits of Eta invariants, Rho invariants of the total space of a fiber bundle are investigated. One concern is to formulate the aspects of local index theory for families of Dirac operator in terms of the odd signature…
We discuss an universal bordism invariant obtained from the Atiyah-Patodi-Singer eta-invariant from the analytic and homotopy theoretic point of view. Classical invariants like the Adams e-invariant, $\rho$-invariants and $String$-bordism…
In his 2005 paper, S.T. Smith proposed an intrinsic Cram\'er-Rao bound on the variance of estimators of a parameter defined on a Riemannian manifold. In the present technical note, we consider the special case where the parameter lives in a…
Based on the Atiyah-Patodi-Singer index formula, we construct an obstruction to positive scalar curvature metrics with mean convex boundaries on spin manifolds of infinite K-area. We also characterize the extremal case. Next we show a…
Let $(X_0,\mathcal{F}_0) $ be a compact manifold with boundary endowed with a foliation $\mathcal{F}_0$ which is assumed to be measured and transverse to the boundary. We denote by $\Lambda$ a holonomy invariant transverse measure on…
It is shown that for any piecewise-linear closed orientable manifold of odd dimension there exists an invariantly defined metric on the determinant line of cohomology with coefficients in an arbitrary flat bundle E over the manifold (E is…
In previous work, we introduced eta invariants for even dimensional manifolds. It plays the same role as the eta invariant of Atiyah-Patodi-Singer, which is for odd dimensional manifolds. It is associated to $K^1$ representatives on even…
We establish enhanced bounds on Cheeger-Gromov rho-invariants for general 3-manifolds and yet stronger bounds for special classes of 3-manifold. As key ingredients, we construct chain null-homotopies whose complexity is linearly bounded by…