The eta invariant (some recent developments)
The ...-form and a generalized Maslov index.
The generalized Lichnerowicz formula and analysis of Dirac operators.
The heat equation in riemannian geometry
The Index of Manifolds with Toral Actions and Geometric Interpretations of the ... (..., (S1, Mn)) Invariant of Atiyah and Singer.
The index of signature operators on Lipschitz manifolds
The index of transversally elliptic complexes
The local index density of the perturbed de Rham complex
A perturbation of the de Rham complex was introduced by Witten for an exact 1-form and later extended by Novikov for a closed 1-form on a Riemannian manifold . We use invariance theory to show that the perturbed index density is independent of ; this result was established previously by J. A. Álvarez López, Y. A. Kordyukov and E. Leichtnam (2020) using other methods. We also show the higher order heat trace asymptotics of the perturbed de Rham complex exhibit nontrivial dependence on . We establish...
The Logarithm of the Dedekind n-Function.
The Residue of the Local Eta Function at the Origin.
The Scalar Curvature and the Spectrum of the Laplacian of Spin Manifolds.
The signature package on Witt spaces
In this paper we prove a variety of results about the signature operator on Witt spaces. First, we give a parametrix construction for the signature operator on any compact, oriented, stratified pseudomanifold which satisfies the Witt condition. This construction, which is inductive over the ‘depth’ of the singularity, is then used to show that the signature operator is essentially self-adjoint and has discrete spectrum of finite multiplicity, so that its index—the analytic signature of —is well-defined....
The Yang-Mills equations and the topology of 4-manifolds
Transgressed Euler classes of vector bundles, adiabatic limits of eta invariants and special values of -functions
Un théorème de l'indice relatif
Une approche probabiliste du théorème de l'indice (Atiyah-Singer)
Une suite exacte en -cohomologie
Vector bundles, ellipticity and index theorem.
Vector Bundles on Projective 3-Space.
Von Neumann Spectra Near Zero.