Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, we prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra.
History
Citation
Carey, A. L., Gayral, V., Rennie, A. C. & Sukochev, F. A. (2014). Index theory for locally compact noncommutative geometries. Memoirs of the American Mathematical Society, 231 (1085), 1-131.