Lecture 20

Representing Covering Spaces by Permutations, pp. 68--70

Cover all of the material in the subsection on "Representing Covering Space by Permutations" (pp. 68--70). In particular, your goal will be to show that n-sheeted covering spaces of X are classified by equivalence classes of homomorphisms of π1(X,x0) to Σn where Σn is the symmetric on n symbols and the equivalence relation identifies a homomorphism with its "conjugates."