SPECTRAL TRIPLES WITH NON-PRODUCT DIRAC OPERATORS

Models of noncommutative geometry that are beyond the usual almost-commutative framework that assumes product metrics may lead to interesting
physical theories in  both particle physics and gravity. In the former, they allow a description of the Standard Model without the fermion doubling, with topological terms, and  the explicit violation of the CP-symmetry. A similar approach applied to the latter gives an interesting version of gravity with two metrics. Based on joint works with Arkadiusz Bochniak and Paweł Zalecki.