Related papers: Triplets spectraux en geometrie d'Arakelov
In Arakelov theory a completion of an arithmetic surface is achieved by enlarging the group of divisors by formal linear combinations of the ``closed fibers at infinity''. Manin described the dual graph of any such closed fiber in terms of…
In this survey, written for the proceedings of the VII meeting of the CNTA held in May 2002 in Montreal, we describe how Connes' theory of spectral triples provides a unified view, via noncommutative geometry, of the archimedean and the…
A fundamental tool in noncommutative geometry is Connes' character formula. This formula is used in an essential way in the applications of noncommutative geometry to index theory and to the spectral characterisation of manifolds. A…
We use topological methods to study various semicontinuity properties of spectra of singular points of plane algebraic curves and of polynomials in two variables at infinity. Using Seifert forms and the Tristram--Levine signatures of links,…
The Image-Computing Spectral Sequence computes the homology of the image of a finite map from the alternating homology of the multiple point spaces of the map. A related spectral sequence was obtained by Gabrielov, Vorobjob and Zell which…
Archimedean cohomology provides a cohomological interpretation for the calculation of the local L-factors at archimedean places as zeta regularized determinant of a log of Frobenius. In this paper we investigate further the properties of…
The aim of this paper is to construct and examine three candidates for local-to-global spectral sequences for the cohomology of diagrams of algebras with directed indexing. In each case, the $E^2$ -terms can be viewed as a type of local…
In the context of A. Connes' spectral triples, a suitable notion of morphism is introduced. Discrete groups with length function provide a natural example for our definitions. A. Connes' construction of spectral triples for group algebras…
This is the second paper in a series of three papers aiming to study cohomology of group theoretic Dehn fillings. In the present paper, we derive a spectral sequence for Cohen-Lyndon triples which can be thought of as a refined version of…
We give a geometrical construction of Connes spectral triples or noncommutative Dirac operators $D$ starting with a bimodule connection on the proposed spinor bundle. The theory is applied to the example of $M_2(\Bbb C)$, and also applies…
It is known that the spin structure on a Riemannian manifold can be extended to noncommutative geometry using the notion of a spectral triple. For finite geometries, the corresponding finite spectral triples are completely described in…
This paper generalizes Manin's approach towards a geometrical interpretation of Arakelov theory at infinity to linear cycles on projective spaces. We show how to interpret certain non-Archimedean Arakelov intersection numbers of linear…
We explain how a simple twisting of the notion of spectral triple allows to incorporate type III examples, such as those arising from the transverse geometry of codimension one foliations. Since the twisting of the commutators turns the…
Our work is concerned with simplicial complexes that describe higher-order interactions in real complex systems. This description allows to go beyond the pairwise node-to-node representation that simple networks provide and to capture a…
We prove a local index formula in conformal geometry by computing the Connes-Chern character for the conformal Dirac (twisted) spectral triple recently constructed by Connes-Moscovici. Following an observation of Moscovici, the computation…
For a unital C*-algebra A, which is equipped with a spectral triple and an extension T of A by the compacts, we construct a family of spectral triples associated to T and depending on the two positive parameters (s,t). Using Rieffel's…
As an outgrowth of our investigation of non-regular spaces within the context of quantum gravity and non-commutative geometry, we develop a graph Hilbert space framework on arbitrary (infinite) graphs and use it to study spectral properties…
We construct the analogue of the Serre spectral sequence for the bounded cohomology of simplicial sets with seminormed local coefficients. As applications, we obtain a (non-isometric) generalization of Gromov's mapping theorem and some…
We generalise the local index formula of Connes and Moscovici to the case of spectral triples for a *-subalgebra \A of a general semifinite von Neumann algebra. In this setting it gives a formula for spectral flow along a path joining an…
The notion of a spectral geometry on a compact metric space X is introduced. This notion serves as a discrete approximation of X motivated by the notion of a spectral triple from non-commutative geometry. A set of axioms charaterising…