Ponge, Raphaël; Wang, Hang Noncommutative geometry and conformal geometry: I. Local index formula and conformal invariants. (English) Zbl 1417.58005 J. Noncommut. Geom. 12, No. 4, 1573-1639 (2018). This paper is part of a series of papers applying techniques of noncommutative geometry in the settings of conformal geometry and noncommutative versions of conformal geometry. In this interesting paper, the authors give the reformulation of the local index formula in conformal geometry in such a way to take into account the action of conformal diffeomorphisms. Moreover, they construct and compute a whole new families of geometric conformal invariants attached with conformal diffeomorphisms. Reviewer: Yong Wang (Changchun) Cited in 9 Documents MSC: 58B34 Noncommutative geometry (à la Connes) 53A30 Conformal differential geometry (MSC2010) 58J20 Index theory and related fixed-point theorems on manifolds 19D55 \(K\)-theory and homology; cyclic homology and cohomology 55N91 Equivariant homology and cohomology in algebraic topology Keywords:noncommutative geometry; conformal geometry; index theory; cyclic homology; equivariant cohomology PDFBibTeX XMLCite \textit{R. Ponge} and \textit{H. Wang}, J. Noncommut. Geom. 12, No. 4, 1573--1639 (2018; Zbl 1417.58005) Full Text: DOI arXiv References: [1] A. Alexakis, {\it The decomposition of global conformal invariants}, Annals of Mathematics Studies, 182, Princeton University Press, Princeton, NJ, 2012.Zbl 1258.53003 MR 2918125 · Zbl 1258.53003 [2] M. F. Atiyah and R. Bott, A Lefschetz fixed point formula for elliptic complexes. I, {\it Ann.} {\it of Math. 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