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Geometry of pseudoriemannian spaces and its application in field theory

Final Activity Report Summary - GPSAFT (Geometry of pseudoriemannian spaces and its application in field theory)

The main results of the project included:

1. the construction of spectral triples on a large family of non-commutative objects, including the quantum three-sphere
2. the construction of different spin structures on non-commutative tori
3. the construction of indefinite-type metrics of quantum three-sphere
4. the calculation of Hochschild and cyclic homologies on quantum hyperplanes.

These were the fundamental steps, as was the main objective of the first year of the long-term project. The future research steps would be the analysis of field-theory models and Riemannian geometry, and were under investigation by the time of the project completion.