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Heat Trace and Spectral Action on the Standard Podleś Sphere

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Abstract

We give a new definition of dimension spectrum for non-regular spectral triples and compute the exact (i.e., not only the asymptotics) heat-trace of standard Podleś spheres \({S^2_q}\) for 0 < q < 1, study its behaviour when \({q\to 1}\) , and fully compute its exact spectral action for an explicit class of cut-off functions.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Jagiellonian University, łojasiewicza 6, 30-348, Kraków, Poland

    Michał Eckstein

  2. Laboratoire affilié à la Frumam FR7332, Aix Marseille Université, CNRS et Université de Toulon, CPT, UMR 7332, 13288, Marseille, France

    Bruno Iochum

  3. Institute of Physics, Jagiellonian University, Reymonta 4, 30-059, Kraków, Poland

    Andrzej Sitarz

  4. Institute of Mathematics of the Polish Academy of Sciences, Śniadeckich 8, 00-950, Warsaw, Poland

    Andrzej Sitarz

Authors
  1. Michał Eckstein
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  2. Bruno Iochum
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  3. Andrzej Sitarz
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Corresponding author

Correspondence to Bruno Iochum.

Additional information

Communicated by A. Connes

A. Sitarz: Partially supported by NCN grant 2011/01/B/ST1/06474.

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Eckstein, M., Iochum, B. & Sitarz, A. Heat Trace and Spectral Action on the Standard Podleś Sphere. Commun. Math. Phys. 332, 627–668 (2014). https://doi.org/10.1007/s00220-014-2054-5

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  • DOI: https://doi.org/10.1007/s00220-014-2054-5

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