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.