The ball is a manifold in ;

orient it naturally and give

the induced orientation. Assume that is a defined in such that

for each ,

a) Given , let be the manifold in consisting of all with , oriented naturally. Find .

b) If , what can you say about and ?

c) If for some in , what can you say about and ?

*Munkres. Chapter 7. Paragraph 37. Problem 5.