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Asymptotic equivariant index of Toeplitz operators and relative index of CR structures

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Geometric Aspects of Analysis and Mechanics

Part of the book series: Progress in Mathematics ((PM,volume 292))

Abstract

Using equivariant Toeplitz operator calculus, we give a new proof of the Atiyah–Weinstein conjecture on the index of Fourier integral operators and the relative index of CR structures.

Mathematics Subject Classification (2010): Primary: 58J20; Secondary: 19L47, 32A45, 53D10, 58J40

Research partially supported by NSF Grant 0703775

Research partially supported by NSF Grant 0707137

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Author information

Authors and Affiliations

  1. Institut de Mathématiques de Jussieu-UMR7586, UPMC-Paris 6, 4, place Jussieu, F-75005, Paris, France

    Louis Boutet de Monvel

  2. Institut de Mathématiques de Jussieu-UMR7586, CNRS, 4, place Jussieu, F-75005, Paris, France

    Eric Leichtnam

  3. Department of Mathematics, Washington University, St. Louis, MO, 63130, USA

    Xiang Tang

  4. Department of Mathematics, University of California, Berkeley, CA, 94720, USA

    Alan Weinstein

Authors
  1. Louis Boutet de Monvel
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  2. Eric Leichtnam
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  3. Xiang Tang
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  4. Alan Weinstein
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Corresponding author

Correspondence to Louis Boutet de Monvel .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Utrecht University, P.O. Box 80.010, Utrecht, 3508 TA, Netherlands

    Johan A.C. Kolk

  2. Mathematical Institute, Utrecht University, P.O. Box 80.010, Utrecht, 3508 TA, Netherlands

    Erik P. van den Ban

Additional information

This paper is dedicated to J.J. Duistermaat for his 65th birthday

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de Monvel, L.B., Leichtnam, E., Tang, X., Weinstein, A. (2011). Asymptotic equivariant index of Toeplitz operators and relative index of CR structures. In: Kolk, J., van den Ban, E. (eds) Geometric Aspects of Analysis and Mechanics. Progress in Mathematics, vol 292. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8244-6_2

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