Jianfeng Lin: Configuration spaces and diffeomorphism groups of 4-manifolds
Jianfeng Lin: Configuration spaces and diffeomorphism groups of 4-…
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Let φ: S1 →S2 be a diffeomorphism. a. Show that S1 is orientable if and only if S2 is orientable (thus, orientability is preserved by diffeomorphisms. b. Let S1 and S2 be orientable and oriented. Prove that the diffeomorphism φinduces an orientation in S2. Use the antipodal map of the sphere (Exercise 1, Sec. 2-3 ) to show that this orientation may be distinct (cf. Exercise 4 ) from the initial one (thus, orientation itself may not be preserved by diffeomorphisms; note, however, that if S1 and S
Let φ: S1 →S2 be a diffeomorphism. a. Show that S1 is orientable if an…
Aug 11, 2020
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