Sentence examples for fundamental groups of from inspiring English sources

Hence the well known fact that the set of fundamental groups of smooth projective varieties is just the set of fundamental groups of smooth algebraic surfaces.

We then briefly discuss Kodaira's problem and Voisin's counterexamples, then we dwell on fundamental groups of projective varieties, and on the Shafarevich conjecture.

These subgroups are realized as the fundamental groups of a number of 2-complexes naturally associated to the biorder structure of the set of idempotents.

Figure 13[2] The class of hyperbolic groups is large and includes important subkinds, such as finite groups, free groups and the fundamental groups of surfaces of genus \ \ge 2\).

(5) Even if not useful for computations, one can still interpret the exact sequence as an exact sequence for the fundamental groups of a tower of covering spaces, using the standard construction for equivariant cohomology that we shall discuss later.

There are positive results, which answer the Shafarevich question in affirmative provided the fundamental group of X satisfies certain properties, related somehow to some of the themes treated in this article, which is the existence of certain homomorphisms to fundamental groups of classifying spaces, and to the theory of harmonic maps.

Let π be the fundamental group of a connected finite graph of groups with finitely generated vertex groups GP.

Conversely (see [333], p. 180), Any finitely presented group (Gamma ) is the fundamental group of a compact oriented 4-manifold4-manifold

Now, the Shafarevich question has a positive answer if the fundamental group of (hat{X} ), the image of the fundamental group of a general fibre F inside (pi _1(X)), is finite.

In [15], Milnor proved that the fundamental group of a compact Riemannian manifold of negative sectional curvature has exponential growth.

Moreover, since the fundamental group of a torus is torsion free, we can actually conclude that (T=0).