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On fundamental groups of algebraic varieties and value distribution theory

Katsutoshi Yamanoi (2010)

Annales de l’institut Fourier

If a smooth projective variety X admits a non-degenerate holomorphic map X from the complex plane , then for any finite dimensional linear representation of the fundamental group of X the image of this representation is almost abelian. This supports a conjecture proposed by F. Campana, published in this journal in 2004.

On the Fundamental Group of self-affine plane Tiles

Jun Luo, Jörg M. Thuswaldner (2006)

Annales de l’institut Fourier

Let A 2 × 2 be an expanding matrix, 𝒟 2 a set with | det ( A ) | elements and define 𝒯 via the set equation A 𝒯 = 𝒯 + 𝒟 . If the two-dimensional Lebesgue measure of 𝒯 is positive we call 𝒯 a self-affine plane tile. In the present paper we are concerned with topological properties of 𝒯 . We show that the fundamental group π 1 ( 𝒯 ) of 𝒯 is either trivial or uncountable and provide criteria for the triviality as well as the uncountability of π 1 ( 𝒯 ) . Furthermore, we give a short proof of the fact that the closure of each component of int ( 𝒯 ) is a locally...

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