It is equivalent to say G act transitively on p -1 (x) ∈ X if p is normal, which related to theorem of unique lifting for covering spaces. If the fibre of x ∈ X 0 is a constant n, then this normal covering is called n-sheeted. Definition 3.2 (Covering operator and induced homomorphism). Let p : X → X/G be any normal covering map from a topological space to its quotient space, then, one can define a homomorphism over chain complexes: