Target Audience and Prerequisites. The mathematical philosophy of index theory and all its
basic concepts, technicalities and applications are explained in Parts I-III. Those are the …

Let G be a connected, linear real reductive group. We give sufficient conditions ensuring the
well-definedness of the delocalized eta invariant\(\eta _g (D_X)\) associated to a Dirac …

We study index theory of G-invariant elliptic pseudo-differential operators acting on a
complete Riemannian manifold, where a unimodular, locally compact group G acts properly …

On a closed smooth manifold, we consider operator families being linear combinations of
parameter-dependent pseudodifferential operators with periodic coefficients. Such families …

Abstract We prove a Godbillon–Vey index formula for longitudinal Dirac operators on a
foliated bundle with boundary (X, F); in particular, we define a Godbillon–Vey eta invariant …

This paper is the second part of a series of papers on noncommutative geometry and
conformal geometry. In this paper, we compute explicitly the Connes–Chern character of an …

Let $\Gamma $ be a compact group acting on a smooth, compact manifold $ M $, let $
P\in\psi^ m (M; E_0, E_1) $ be a $\Gamma $-invariant, classical pseudodifferential operator …

We prove an index theorem of Atiyah–Singer type for Dirac operators on manifolds with a
Lie structure at infinity (Lie manifolds for short). With the help of a renormalized supertrace …

На гладком замкнутом многообразии рассматривается семейство операторов вида
линейной комбинации псевдодифференциальных операторов с параметром с …

Let be a finitely generated discrete group satisfying the rapid decay condition. We give a
new proof of the higher Atiyah–Patodi–Singer theorem on a Galois-coverings, thus providing …