Exercise 4. Let X = C {1} and Y = C {/2+k, k Z} and...

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Exercise 4. Let X = C\ {±1} and Y = C\ {π/2+πk, k € Z} and consider the covering sin: Y → X. We define (a) Compute f ○ fe, fk fk(z) = 2 + 2πk, ke Z 9k (2) = π = 2+2πk, kЄZ ge, 9k fe, Gk gl. sin (b) Show that Deck (Y S, X) = {fk, ge : k, l = Z}. (c) Describe Deck (Y sin, X) as a semi-direct product. 25 P. Exercise 4. Let X = C\ {±1} and Y = C\ {π/2+πk, k € Z} and consider the covering sin: Y → X. We define (a) Compute f ○ fe, fk fk(z) = 2 + 2πk, ke Z 9k (2) = π = 2+2πk, kЄZ ge, 9k fe, Gk gl. sin (b) Show that Deck (Y S, X) = {fk, ge : k, l = Z}. (c) Describe Deck (Y sin, X) as a semi-direct product. 25 P.

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a We compute fi fe fk ge fi fe z 2i 2e z 2i e fk ge z 2k 2g z 2k g b To show that DeckY sin X fk ge kl Z we must show that each element of the set is ... View the full answer