In this note, we use Connes’ theory of spectral triples to provide a connection between Manin’s model of the dual graph of the fiber at infinity of an Arakelov surface and the cohomology of the mapping cone of the local monodromy. Abridged English version In Arakelov theory a completion of an arithmetic surface is achieved by enlarging the group of divisors by formal linear combinations of the ...

To a finite, connected, unoriented graph of Betti-number g ≥ 2 and valencies ≥ 3 we associate a finitely summable, commutative spectral triple (in the sense of Connes), whose induced zeta functions encode the graph. This gives another example where noncommutative geometry provides a rigid framework for classification.

It is well-known that a compact Riemannian spin manifold (M, g) can be reconstructed from its canonical spectral triple (C∞(M), L2(M,ΣM),D) where ΣM denotes the spinor bundle and D the Dirac operator. We show that g can be reconstructed up to conformal equivalence from (C∞(M), L2(M,ΣM), sign(D)).

We perform the Batalin-Vilkovisky quantization of Yang–Mills theory on a 2-point space, discussing the formulation of Connes–Lott as well as Connes’ real spectral triple approach. Despite of the model’s apparent simplicity the gauge structure reveals infinite reducibility and the gauge fixing is afflicted with the Gribov problem. 1

We show that elliptic solutions of classical Yang-Baxter equation (CYBE) can be obtained from triple Massey products on elliptic curve. We introduce the associative version of this equation which has two spectral parameters and construct its elliptic solutions. We also study some degenerations of these solutions.

An AF C*-algebra has a natural filtration as an increasing sequence of finite dimensional C*-algebras. We show that it is possible to construct a Dirac operator which relates to this filtration in a natural way and which will induce a metric for the weak*-topology on the state space of the algebra. In the particular case of a UHF C*algebra the construction can be made in a way, which relates di...

A distributed-feedback dye laser with a quenching cavity was designed and constructed for generating a tunable picosecond pulse with a narrow spectral linewidth. This nearly transform-limited pulse was succeedingly amplified by a triple-pass off-axis amplifier. The pulse duration and the spectral linewidth were 60 ps and 9.4 pm, respectively. The amplified pulse was frequency-doubled by second-...

The torus group (S) has a canonical action on the odd dimensional sphere S q . We take the natural Hilbert space representation where this action is implemented and characterize all odd spectral triples acting on that space and equivariant with respect to that action. This characterization gives a construction of an optimum family of equivariant spectral triples having nontrivial K-homology cla...

The concept of a spectral triple (unbounded Fredholm module) due to A.Connes ([Co1]) is a natural noncommutative generalisation of a notion of a compact manifold, with certain summability properties corresponding in the classical case to the dimension of the manifold. Recently E.Christensen and C. Ivan established the existence of spectral triples on arbitrary AF algebras ([CI]). In this note w...

We analyse the NC-space underlying the quantum group SUq(2) from the spectral point of view which is the basis of noncommutative geometry, and show how the general theory developped in our joint work with H. Moscovici applies to the specific spectral triple defined by Chakraborty and Pal. This provides the pseudo-differential calculus, the Wodzciki-type residue, and the local cyclic cocycle giv...