Question: I am trying to answer this question. Any help is appreciated! (2) Let B, be the circle (r + 1)? + 1? = 1, A,

I am trying to answer this question. Any help is appreciated!

 I am trying to answer this question. Any help is appreciated!

(2) Let B, be the circle (r + 1)? + 1? = 1, A, be the circle (r - 1)3 + 1? = 1, An be the circle (x + 3)2 + 1? = 1 and Bo be the circle (r - 3)? + 1 = 1. Define X = Ao U B, U A, U Bo, and X = BIU Al. Define a map p: X - X as follows: p wraps B, around B, twice and wraps At around A, twice; Bo and An are mapped homeomorphically onto B, and A, respectively. a) Give a presentation for mi(X, (0,0)) and 71(X, (0,0)). Carefully write down the generators. b) Compute p. (71(X, (0,0)) as a subgroup of "(X, (0,0)). c) What is the automorphism group A(X, p)? Give reasons. d) Is p. (1 (X, (0, 0) ) a normal subgroup of m(X, (0, 0))? Give reasons

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