1995/01/01 by Alain Connes, Henri Moscovici · 5 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Noncommutative and Quantum Gravity Theories
paper · doi:10.1007/978-3-0348-9102-8_4
openalex publication_date 1995/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
In noncommutative geometry a geometric space is described from a spectral vantage point, as a triple ( A, H, D ) consisting of a *-algebra A represented in a Hilbert space H together with an unbounded selfadjoint operator D , with compact resolvent, which interacts with the algebra in a bounded fashion. This paper contributes to the advancement of this point of view in two significant ways: (1) by showing that any pseudogroup of transformations of a manifold gives rise to such a spectral triple of finite summability degree, and (2) by proving a general, in some sense universal, local index formula for arbitrary spectral triples of finite summability degree, in terms of the Dixmier trace and its residue-type extension. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.