Carlos Simpson

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The fundamental group is one of the most basic topological invariants of a space. The aim of this paper is to present a method of constructing representations of fundamental groups in complex geometry, using techniques of partial differential equations. A representation of the fundamental group of a manifold is the same thing as a vector bundle over the(More)
The purpose of this paper is to extend the correspondence between Higgs bundles and local systems [2,5,6,7, 13, 17, 19,20,21] to the case when X is a noncom pact algebraic curve. The basic result is that there is a class of analytic objects on X which will be put in one-to-one correspondences with two different classes of algebraic geometric objects on the(More)
Whereas usual Hodge theory concerns mainly the usual or abelian cohomology of an algebraic variety—or eventually the rational homotopy theory or nilpotent completion of π1 which are in some sense obtained by extensions—nonabelian Hodge theory concerns the cohomology of a variety with nonabelian coefficients. Because of the basic fact that homotopy groups in(More)
Let X be a compact connected Kähler manifold, x ∈ X and Γ = π1(X,x). Let ρ : Γ → GLN (C) be a finite dimensional semisimple representation. We assume ρ to be the monodromy of a given polarized C-VHS (Vρ,F ,G • , S) whose weight is zero. If ρ is not irreducible then several distinct polarizations could be chosen, we fix one once for all. In the introduction,(More)
© Publications mathématiques de l’I.H.É.S., 1994, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression(More)
© Publications mathématiques de l’I.H.É.S., 1992, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression(More)
In [2] Baez and Dolan established their stabilization hypothesis as one of a list of the key properties that a good theory of higher categories should have. It is the analogue for n-categories of the well-known stabilization theorems in homotopy theory. To explain the statement, recall that Baez-Dolan introduce the notion of k-uply monoidal n-category which(More)
The purpose of this paper is to develop some additional techniques for the weak ncategories defined by Tamsamani in [27] (which he calls n-nerves). The goal is to be able to define the internal Hom(A,B) for two n-nerves A and B, which should itself be an n-nerve. This in turn is for defining the n+ 1-nerve nCAT of all n-nerves conjectured in [27], which we(More)
The purpose of this paper is to introduce the notion of mixed twistor structure as a generalization of the notion of mixed Hodge structure. Recall that a mixed Hodge structure is a vector space V with three filtrations F , F ′ and W (the first two decreasing, the last increasing) such that the two filtrations F and F ′ induce i-opposed filtrations on Gr i(More)