Manifold and Orbifold Constructions

Abstract

AbstractIn this chapter, we collect some information on various constructions of manifolds, orbifolds, and their covers. Notably, we discuss the notions of fiber product (in the sense of Thurston) and compositum of manifolds over a common developable orbifold, the difference with the set-theoretic fiber product, the connected components of the fiber product, compositum of Galois covers, normal closure of a cover, and the relation between commensurability, arithmeticity, and the existence of certain covers in relation to Mostow rigidity.