Homotopy properties of algebraic vector bundles.
If a smooth projective variety admits a non-degenerate holomorphic map from the complex plane , then for any finite dimensional linear representation of the fundamental group of the image of this representation is almost abelian. This supports a conjecture proposed by F. Campana, published in this journal in 2004.
Let be an expanding matrix, a set with elements and define via the set equation . If the two-dimensional Lebesgue measure of is positive we call a self-affine plane tile. In the present paper we are concerned with topological properties of . We show that the fundamental group of is either trivial or uncountable and provide criteria for the triviality as well as the uncountability of . Furthermore, we give a short proof of the fact that the closure of each component of is a locally...