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Jet isomorphism for conformal geometry

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C. Robin Graham
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** Address.**
Department of Mathematics, University of Washington

Box 354350, Seattle, WA 98195-4350, USA

** E-mail:**
robin@math.washington.edu

**Abstract.**
Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite order ambient lift for conformal densities in the case in which harmonic extension is obstructed is described. A jet isomorphism theorem for even dimensional conformal geometry is formulated using the inhomogeneous ambient metrics recently introduced by the author and K. Hirachi.

**AMSclassification. ** 53B20.

**Keywords. **Conformal geometry, ambient metric, jet isomorphism, deformation complex.