Geometric Construction of the Covering Manifold

Abstract In this chapter, we provide a geometric construction of manifold extending given Galois cover to wreath product, using composita and fiber products. For be possible, certain assumption on the homology, previously called (∗), needs strengthened new condition (∗∗) (equivalent in most cases). To motivate use condition, first recall connection between homology quotient coinvariants. Apart from tools, is also based vanishing group cohomology, which used prove existence isometries manifolds. final section, give universal property product relation coverings manifolds, just like there such theory extensions fields.