We compute the spectral action of SU(2)/ with the trivial spin structure and the round metric and find it in each case to be equal to . We do this by explicitly computing the spectrum of the Dirac operator for SU(2)/ equipped with the trivial spin structure and a selection of metrics. Here is a finite subgroup of SU(2). In the case where is cyclic, or dicyclic, we consider the one-parameter family of Berger metrics, which includes the round metric, and when is the binary tetrahedral, binary octahedral or binary icosahedral group, we only consider the case of the round metric.
Cite this article
Kevin Teh, Nonperturbative spectral action of round coset spaces of SU(2). J. Noncommut. Geom. 7 (2013), no. 3, pp. 677–708DOI 10.4171/JNCG/131