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arXiv · 1709.08082

Motives and periods in Bianchi IX gravity models

Wentao Fan·Farzad Fathizadeh·Matilde Marcolli
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Abstract

We show that, when considering the anisotropic scaling factors and their derivatives as affine variables, the coefficients of the heat kernel expansion of the Dirac-Laplacian on $SU(2)$ Bianchi IX metrics are algebro-geometric periods of motives of complements in affine spaces of unions of quadrics and hyperplanes. We show that the motives are mixed Tate and we provide an explicit computation of their Grothendieck classes.

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Wentao Fan, Farzad Fathizadeh, Matilde Marcolli. 2017-09-23. Motives and periods in Bianchi IX gravity models. https://doi.org/10.1007/s11005-018-1096-6

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