The local index formula in semifinite Von Neumann algebras I: Spectral flow
TLDR
In this article, the authors generalize the local index formula of Connes and Moscovici to the case of spectral triples for a * -subalgebra A of a general semi-neumann algebra.About:
This article is published in Advances in Mathematics.The article was published on 2006-06-01 and is currently open access. It has received 113 citations till now. The article focuses on the topics: Affiliated operator & Von Neumann algebra.read more
Citations
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Noncommutative Geometry, Quantum Fields and Motives
Alain Connes,Matilde Marcolli +1 more
TL;DR: In this article, the Riemann zeta function and non-commutative spaces are studied in the context of quantum statistical mechanics and Galois symmetries, including the Weil explicit formula.
Book
Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
TL;DR: In this article, the topological invariants of topological solid state systems are discussed. But invariants are defined as measurable quantities and invariants do not necessarily imply invariants.
Book
An Introduction to Noncommutative Geometry
TL;DR: In this paper, a course on non-commutative geometry from the non-computative point of view was presented at the 1997 Summer School on Non-Commutative Geometry and Applications at the European Mathematical Society (EMS) at Monsaraz and Lisboa, Portugal, September 1-10, 1997.
Book ChapterDOI
The Local Index Formula in Noncommutative Geometry
TL;DR: In this article, the authors present a proof of the Connes-Moscovici index formula, expressing the index of a (twisted) operator in a spectral triple by a local formula.
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Noncommutative Geometry and Particle Physics
TL;DR: The non-commutative geometry of Yang-Mills fields has been studied in this article, where the local index formula in non-convex geometry has been defined.
References
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A comprehensive introduction to differential geometry
TL;DR: Spivak's comprehensive introduction to differential geometry as discussed by the authors takes as its theme the classical roots of contemporary differential geometry, and explains why it is absurdly inefficient to eschew the modern language of manifolds, bundles, forms, etc., which was developed precisely to rigorize the concepts of classical differential geometry.
Journal ArticleDOI
Non-commutative differential geometry
Alain Connes,Alain Connes +1 more
TL;DR: In this paper, the authors present a legal opinion on the applicability of commercial or impression systématiques in the context of the agreement of publication mathématique de l'I.H.É.S.
Book ChapterDOI
Non-Commutative Geometry
TL;DR: For purely mathematical reasons, it is necessary to consider spaces which cannot be represented as point set sand where the coordinates describing the space do not commute as mentioned in this paper, i.e., spaces which are described by algebras of coordinates which are not commutative.