Unformatted text preview: n ) is a matrix of dimension n ( n − 1) / 2 (you already showed it has two components in HW #1). 5. [Guillemin and Pollack, page 18, #6; MTA 3.5-5] (a) If f and g are submersions/immersions, show that f × g is. (b) If f and g are submersions/immersions, show that g ◦ f is. (c) If f is an immersion, show that its restriction to any submanifold of its domain is an immersion. (d) When dim M = dim N , show that submersions/immersions f : M → N are the same as local di²eomorphisms. 6. MTA 3.5-11: covering maps....
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- Fall '08
- Continuous function, Exponentiation, Manifold