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      Noncommutative residue invariants for CR and contact manifolds

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          Abstract

          In this paper we produce several new invariants for CR and contact manifolds by looking at the noncommutative residue traces of various geometric projections. In the CR setting these operators arise from the Kohn-Rossi complex and include the Szeg\"o projections on forms. In the contact setting they stem from the generalized Szeg\"o 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 answer a question of Fefferman.

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          Author and article information

          Journal
          04 October 2005
          2006-07-21
          Article
          math/0510061
          Custom metadata
          Primary 32A25; Secondary 32V20, 53D35, 58J40, 58J42
          J. Reine Angew. Math. (Crelle's Journal) 614 (2008) 117-151.
          v4: new CR invariants with coefficients in CR holomorphic vector bundles + more comments about computation of the invariants + new title; 32 pages
          math.DG math.CV

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