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A Construction of Critical GJMS Operators Using Wodzicki's Residue

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Abstract

For an even dimensional, compact, conformal manifold without boundary we construct a conformally invariant differential operator of order the dimension of the manifold. In the conformally flat case, this operator coincides with the critical GJMS operator of Graham-Jenne-Mason-Sparling. We use the Wodzicki residue of a pseudo-differential operator of order −2, originally defined by A. Connes, acting on middle dimension forms.

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  1. Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN, 47907-2067, USA

    William J. Ugalde

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  1. William J. Ugalde
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Correspondence to William J. Ugalde.

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Communicated by A. Connes

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Ugalde, W. A Construction of Critical GJMS Operators Using Wodzicki's Residue. Commun. Math. Phys. 261, 771–788 (2006). https://doi.org/10.1007/s00220-005-1384-8

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  • DOI: https://doi.org/10.1007/s00220-005-1384-8

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