The covariant systems of Todd and Segre
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 decomposition and specialization of algebraic families of vector bundles
The defect of weak approximation for homogeneous spaces
The degrees of certain strata of the dual variety
The determinant line bundle over moduli spaces of instantons on abelian surfaces.
The differential Galois theory of regular singular p-adic differential equations.
The differential spectrum of a ring
The display locale of a cosheaf
The equations of the abelian surfaces embedded in ...4 (...).
The Etale Homotopy Theorie of a Geometric Fibration.
The Euler characteristic of the moduli space of curves.
The Euler characteristic of varieties realized as the complete intersection of toric hypersurfaces.
The Euler series of restricted Chow varieties
The existence of higher logarithms
The explicit reciprocity law and the cohomology of Fontaine-Messing
The Formal Hodge Filtration.
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...