We present an approximation to topological spaces by noncommutative lattices. This approximation has a deep physical flavour based on the impossibility to fully localize particles in any position measurement. The original space being approximated is recovered out of a projective limit. To appear in ‘Quantum Groups and Fundamental Physical Applications’, ISI Guccia, Palermo, December 1997, D. Ka...

The canonical family of Thom forms s for 0 < s < 1 constructed by Harvey and Lawson on an oriented real vector bundle V ! X with metric connection D V is shown to have a smooth current extension to the bundle of real projective spaces, P(R V) ! X, which compactiies V in the bre directions. The current limit as r ! 1 and s ! 0 of the smooth transgression formula r ? s = r;s is the current equation

Let X be a smooth complex projective variety and A an abelian group. Degree i unramified cohomology H i nr(X,A) of X with coefficients in A can be defined as the direct limit of the sets of data αk ∈ H i B(Uk, A), αk|Uk∩Ul = αl|Uk∩Ul , where the Uk’s are sufficiently small Zariski open sets covering X. Here the notation H i B stands for Betti cohomology of the underlying complex analytic space....

The true prosoluble completion PS(Γ) of a group Γ is the inverse limit of the projective system of soluble quotients of Γ. Our purpose is to describe examples and to point out some natural open problems. We answer the analogue of a question of Grothendieck for profinite completions by providing examples of pairs of non–isomorphic residually soluble groups with isomorphic true prosoluble complet...

In this paper, we use the perspective of linear series, and in particular results following from the degeneration tools of limit linear series, to give a number of new results on existence and non-existence of tamely branched covers of the projective line in positive characteristic. Our results are both in terms of ramification indices and the sharper invariant of monodromy cycles, and the firs...

The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces X,Y are assumed to be polish and equipped with Borel probability measures μ and ν. The transport cost function c : X × Y → [0,∞] is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive meas...

In this paper, we use the perspective of linear series, and in particular results following from the degeneration tools of limit linear series, to give a number of new results on the existence and non-existence of tamely branched covers of the projective line in positive characteristic. Our results are both in terms of ramification indices and the sharper invariant of monodromy cycles, and the ...

We define the height process for super-critical continuous state branching processes with quadratic branching mechanism. It appears as a projective limit of Brownian motions with positive drift reflected at 0 and a > 0 as a goes to infinity. Then we extend the pruning procedure of branching processes to the super-critical case. This give a complete duality picture between pruning and size propo...

Let S be a closed orientable surface with genus g ≥ 2. For a sequence σi in the Teichmüller space of S, which converges to a projective measured lamination [λ] in the Thurston boundary, we obtain a relation between λ and the geometric limit of pants decompositions whose lengths are uniformly bounded by a Bers constant L. We also show that this bounded pants decomposition is related to the Gromo...

1.2. The basic feature that we struggle against is that there are two types of infinite dimensionality at play: pro-infinite dimensionality and ind-infinite dimensionality. That is, we could have an infinite dimensional variety S that is the union S “ YiSi “ colimiSi of finite dimensional varieties, or T that is the projective limit T “ limj Tj of finite dimensional varieties, e.g., a scheme of...