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A perturbation of the de Rham complex was introduced by Witten for an exact 1-form $Θ$ and later extended by Novikov for a closed 1-form on a Riemannian manifold $M$ . We use invariance theory to show that the perturbed index density is independent of $Θ$ ; 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 $Θ$ . We establish...

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The analytic Carathéodory conjecture.

The Atiyah-Patodi-Singer theorem for perturbed Dirac operators on even-dimensional manifolds with bounded geometry.

The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs.

The $b$ -pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem

The cohomology solution and the index theorem on ring surfaces of genus $g$ .

The d-invariant of compact nilmanifolds.

The e-invariant and the spectrum of the Lapacian for compact nilmanifolds covered by Heisenberg groups.

The eta Invariant and ...O of Lens Spaces.

The eta invariant and the K-theory of odd dimensional spherical space forms.

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

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.

Currently displaying 1 – 20 of 23