Using the Chamseddine–Connes approach of the noncommutative action on spectral triples, we show that there are no tadpoles of any order for compact spin manifolds without boundary, and also consider a case of a chiral boundary condition. Using pseudodifferential techniques, we study noncommutative integrals in commutative geometries.
Cite this article
Bruno Iochum, Cyril Levy, Tadpoles and commutative spectral triples. J. Noncommut. Geom. 5 (2011), no. 3, pp. 299–329DOI 10.4171/JNCG/77