Local Index Formula for Quantum Double Suspension

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Abstract

Our understanding of the local index formula in noncommutative geometry has stalled for a while because we do not have more than one explicit computation, namely that of Connes for quantum SU(2), and we do not understand the meaning of the various multilinear functionals involved in the formula. In such a situation further progress in understanding necessitates more explicit computations, and here we execute the second explicit computation for the quantum double suspension, a construction inspired by the Toeplitz extension. More specifically, we compute the local index formula for the quantum double suspensions of \(C(\mathcal {S}^2)\) and the noncommutative 2-torus.

Keywords

Spectral triples Noncommutative geometry Local index formula Quantum double suspension Noncommutative torus 

Mathematics Subject Classification

Primary: 46L87 58B34 Secondary: 19K56 

Notes

Acknowledgements

We would like to thank the anonymous referee for his insightful comments and suggestions.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.The Institute of Mathematical Sciences (HBNI)ChennaiIndia

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