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The Connes Character Formula for Locally Compact Spectral Triples
 
Fedor Sukochev University of New South Wales, Kensington, Australia
Dmitriy Zanin University of New South Wales, Kensington, Australia
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-85629-982-1
Product Code:  AST/445
List Price: $65.00
AMS Member Price: $52.00
Please note AMS points can not be used for this product
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The Connes Character Formula for Locally Compact Spectral Triples
Fedor Sukochev University of New South Wales, Kensington, Australia
Dmitriy Zanin University of New South Wales, Kensington, Australia
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-85629-982-1
Product Code:  AST/445
List Price: $65.00
AMS Member Price: $52.00
Please note AMS points can not be used for this product
  • Book Details
     
     
    Astérisque
    Volume: 4452023; 150 pp
    MSC: Primary 83; 35; 58

    A fundamental tool in noncommutative geometry is Connes's character formula. This formula is used in an essential way in the applications of noncommutative geometry to index theory and to the spectral characterization of manifolds.

    A non-compact space is modeled in noncommutative geometry by a non-unital spectral triple. The authors' aim is to establish Connes's character formula for non-unital spectral triples. This is significantly more difficult than in the unital case, and they achieve it with the use of recently developed double operator integration techniques. Previously, only partial extensions of Connes's character formula to the non-unital case were known.

    In the course of the proof, the authors establish two more results of importance in noncommutative geometry: an asymptotic for the heat semigroup of a non-unital spectral triple and the analyticity of the associated \(\zeta\)-function.

    The authors require certain assumptions on the underlying spectral triple and verify these assumptions in the case of spectral triples associated to arbitrary complete Riemannian manifolds and also in the case of Moyal planes.

    A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

    Readership

    Graduate students and research mathematicians.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 4452023; 150 pp
MSC: Primary 83; 35; 58

A fundamental tool in noncommutative geometry is Connes's character formula. This formula is used in an essential way in the applications of noncommutative geometry to index theory and to the spectral characterization of manifolds.

A non-compact space is modeled in noncommutative geometry by a non-unital spectral triple. The authors' aim is to establish Connes's character formula for non-unital spectral triples. This is significantly more difficult than in the unital case, and they achieve it with the use of recently developed double operator integration techniques. Previously, only partial extensions of Connes's character formula to the non-unital case were known.

In the course of the proof, the authors establish two more results of importance in noncommutative geometry: an asymptotic for the heat semigroup of a non-unital spectral triple and the analyticity of the associated \(\zeta\)-function.

The authors require certain assumptions on the underlying spectral triple and verify these assumptions in the case of spectral triples associated to arbitrary complete Riemannian manifolds and also in the case of Moyal planes.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.