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

Global amoebas are a wide and rich family of graphs that emerged from the study certain Ramsey-Turán problems in 2-colorings edges complete graph Kn deal with appearance unavoidable patterns once amount each color is guaranteed. Indeed, it turns out that, as soon such coloring constraints satisfied if n sufficiently large, then every global amoeba can be found embedded has half its color. Even ...