Teichmüllerraum für total degenerierte Kurven.
The algebraic fundamental group of a reductive group scheme over an arbitrary base scheme
We define the algebraic fundamental group π 1(G) of a reductive group scheme G over an arbitrary non-empty base scheme and show that the resulting functor G↦ π1(G) is exact.
The algebraic topology of smooth algebraic varieties
The closure of a model category
The covering semigroup of invariant control systems on Lie groups
It is well known that the class of invariant control systems is really relevant both from theoretical and practical point of view. This work was an attempt to connect an invariant systems on a Lie group with its covering space. Furthermore, to obtain algebraic properties of this set. Let be a Lie group with identity and a cone in the Lie algebra of that satisfies the Lie algebra rank condition. We use a formalism developed by Sussmann, to obtain an algebraic structure on the covering...
The fundamental group at infinity of affine surfaces.
The fundamental group of a Galois cover of .
The fundamental group of a locally finite graph with ends-a hyperfinite approach
The end compactification |Γ| of a locally finite graph Γis the union of the graph and its ends, endowed with a suitable topology. We show that π₁(|Γ|) embeds into a nonstandard free group with hyperfinitely many generators, i.e. an ultraproduct of finitely generated free groups, and that the embedding we construct factors through an embedding into an inverse limit of free groups. We also show how to recover the standard description of π₁(|Γ|) given by Diestel and Sprüssel (2011). Finally, we give...
The Fundamental Group of the Complement of a Union of Complex Hyperplanes.
The fundamental group of the complement of a union of complex hyperplanes: correction.
The Fundamental Group of the Complement of an Algebraic Curve.
The Fundamental Group-Scheme of an Abelian Variety.
The Hodge de Rham theory of relative Malcev completion
The intrinsic Hodge theory of -adic hyperbolic curves.
The Lefshetz Vanishing Cycles on a Projective Nonsingular Plane Curve.
The Mumford conjecture
The Mumford Conjecture asserts that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra on the Mumford-Morita-Miller characteristic classes; this can be reformulated in terms of the classifying space derived from the mapping class groups. The conjecture admits a topological generalization, inspired by Tillmann’s theorem that admits an infinite loop space structure after applying Quillen’s plus construction. The text presents the proof by Madsen and...
The rational homotopy theory of smooth, complex projective varieties
The tame fundamental group of an abelian variety and integral points
The topological Hawaiian earring group does not embed in the inverse limit of free groups.
Théorème de Van Kampen pour les champs algébriques