# Noncommutative Geometry and Conformal Geometry. I. Local Index Formula and Conformal Invariants

@article{Ponge2014NoncommutativeGA,
title={Noncommutative Geometry and Conformal Geometry. I. Local Index Formula and Conformal Invariants},
author={Raphael Ponge and Han Wang},
journal={arXiv: Differential Geometry},
year={2014}
}
• Published 13 November 2014
• Mathematics
• arXiv: Differential Geometry
This paper is part of a series of articles on noncommutative geometry and conformal geometry. In this paper, we reformulate the local index formula in conformal geometry in such a way to take into account of the action of conformal diffeomorphisms. We also construct and compute a whole new family of geometric conformal invariants associated with conformal diffeomorphisms. This includes conformal invariants associated with equivariant characteristic classes. The approach of this paper involves…
• Mathematics
• 2014
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 equivariant Dirac spectral
• Mathematics
• 2014
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 equivariant Dirac spectral
• Mathematics
• 2016
Twisted spectral triples are a twisting of the notion of spectral triple aiming at dealing with some type III geometric situations. In the first part of the paper, we give a geometric construction of
Twisted spectral triples are a twisting of the notion of spectral triples aiming at dealing with some type III geometric situations. In the first part of the paper, we give a geometric construction
• Mathematics
Ergodic Theory and Dynamical Systems
• 2021
We provide a detailed study of actions of the integers on compact quantum metric spaces, which includes general criteria ensuring that the associated crossed product algebra is again a compact
• Mathematics
• 2020
Given a manifold with boundary endowed with an action of a discrete group on it, we consider the algebra of operators generated by elements in the Boutet de Monvel algebra of pseudodifferential
• Mathematics
Journal of Pseudo-Differential Operators and Applications
• 2021
Given a manifold with boundary endowed with an action of a discrete group on it, we consider the algebra of operators generated by elements in the Boutet de Monvel algebra of pseudodifferential
• Mathematics
Journal of Noncommutative Geometry
• 2019
We investigate the regularity condition for twisted spectral triples. This condition is equivalent to the existence of an appropriate pseudodifferential calculus compatible with the spectral triple.

## References

SHOWING 1-10 OF 91 REFERENCES

This is the fifth in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of “global conformal invariants”; these are defined to be conformally
• Mathematics
• 2014
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 equivariant Dirac spectral
This paper concerns the behavior of conformal diffeomorphisms between Riemannian manifolds, and that of CR diffeomorphisms between strictly pseudoconvex CR manifolds, We develop a new approach to the
• Mathematics
• 2011
In this paper we investigate the curvature of conformal deformations by noncommutative Weyl factors of a flat metric on a noncommutative 2-torus, by analyzing in the framework of spectral triples
• Mathematics
• 1998
Abstract:In this paper we solve a longstanding internal problem of noncommutative geometry, namely the computation of the index of transversally elliptic operators on foliations. We show that the
• Mathematics
• 1987
The conformal Laplacian D = d*d + (n - 2)s/4(n - 1), acting on functions on a Riemannian manifold Mn with scalar curvature s, is a conformally invariant operator. In this paper we will use D to
Green functions play an important role in conformal geometry. In this paper, we explain how to compute explicitly the logarithmic singularities of the Green functions of the conformal powers of the
This is the second in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of global conformal invariants''; these are defined to be conformally