Related papers: The Atiyah-Patodi-Singer index theorem for Dirac o…

This article is a follow up of the previous article of the authors on the analytic surgery of eta- and rho-invariants. We investigate in detail the (Atiyah-Patodi-Singer)-rho-invariant for manifolds with boundary. First we generalize the…

Feynman's time-slicing construction approximates the path integral by a product, determined by a partition of a finite time interval, of approximate propagators. This paper formulates general conditions to impose on a short-time…

Based on operators borrowed from scattering theory, several concrete realizations of index theorems are proposed. The corresponding operators belong to some C*-algebras of pseudo-differential operators with coefficients which either have…

We investigate chiral zero modes and winding numbers at fixed points on $T^2/\mathbb{Z}_N$ orbifolds. It is shown that the Atiyah-Singer index theorem for the chiral zero modes leads to a formula $n_+-n_-=(-V_++V_-)/2N$, where $n_{\pm}$ are…

We study the index of the APS boundary value problem for a strongly Callias-type operator D on a complete Riemannian manifold $M$. We show that this index is equal to an index on a simpler manifold whose boundary is a disjoint union of two…

We define the gauge-equivariant index of a family of elliptic operators invariant with respect to the free action of a family $\GR \to B$ of Lie groups (these families are called ``gauge-invariant families'' in what follows). If the fibers…

Functional determinants for Dirac operators on manifolds with boundary are considered. Ellipticity of boundary value problems is discussed in terms of the Calderon projector. The functional determinant for a Dirac operator on a…

We study general conditions under which the computations of the index of a perturbed Dirac operator $D_{s}=D+sZ$ localize to the singular set of the bundle endomorphism $Z$ in the semi-classical limit $s\to \infty $. We show how to use…

This paper deals with the representations of the fundamental groups of compact surfaces with boundary into classical simple Lie groups of Hermitian type. We relate work on the signature of the associated local systems of…

We show that there is a functor from the category of positive admissible ternary rings to the category of $*$-algebras, which induces an isomorphism of partially ordered sets between the families of $C^*$-norms on the ternary ring and its…

We study the Atiyah-Patodi-Singer (APS) index, and its equality to the spectral flow, in an abstract, functional analytic setting. More precisely, we consider a (suitably continuous or differentiable) family of self-adjoint Fredholm…

For a finite rank projective bundle over a compact manifold, so associated to a torsion, Dixmier-Douady, 3-class, w, on the manifold, we define the ring of differential operators `acting on sections of the projective bundle' in a formal…

For a Dirac-type operator D with a spectral boundary condition, the associated heat operator trace has an expansion in powers and log-powers of t. Some of the log-coefficients vanish in the Atiyah-Patodi-Singer product case. We here…

The purpose of this paper is to compute determinant index bundles of certain families of Real Dirac type operators on Klein surfaces as elements in the corresponding Grothendieck group of Real line bundles in the sense of Atiyah. On a Klein…

A Dirac structure on a vector bundle V is a maximal isotropic subbundle E of the direct sum of V with its dual. We show how to associate to any Dirac structure a Dixmier-Douady bundle A, that is, a Z/2Z-graded bundle of C*-algebras with…

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…

We describe how Lie groupoids are used in singular analysis, index theory and non-commutative geometry and give a brief overview of the theory. We also expose groupoid proofs of the Atiyah-Singer index theorem and discuss the Baum-Connes…

In this work, we study topological properties of surface bundles, with an emphasis on surface bundles with a spin structure. We develop a criterion to decide whether a given manifold bundle has a spin structure and specialize it to surface…

Zero-modes, their topological degeneracy and relation to index theorems have attracted attention in the study of single- and bilayer graphene. For negligible scalar potentials, index theorems explain why the degeneracy of the zero-energy…

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…