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Noncommutative residue invariants for CR and contact manifolds

Abstract In this paper we produce several new invariants for CR and contact manifolds by looking at the noncommutative residue traces of various geometric Ψ H DO projections. In the CR setting these operators arise from the -complex and include the Szegö projections acting on forms. In the contact setting they stem from the generalized Szegö projections at arbitrary integer levels of Epstein-Melrose and from the contact complex of Rumin. In particular, we recover and extend recent results of Hirachi and Boutet de Monvel and we answer a question of Fefferman.