Math 147 - Spring 2014
Homework 2
These problems are due on Thursday, April 17th , at the beginning of class, and will be graded on
clarity of exposition as well as correctness. I encourage you to work in small groups, but what you
hand in must be your ow
Math 147 - Spring 2014
Homework 1
These problems are due on Thursday, April 10th , at the beginning of class, and will be graded on
clarity of exposition as well as correctness. I encourage you to work in small groups, but what you
hand in must be your ow
Math 147 - Spring 2014
Homework 4
These problems are due on Thursday, May 8th , at the beginning of class.
1. Suppose that a compact manifold M is not orientable. Prove that M is not the boundary of
an orientable manifold X.
2. If m < p, show that every m
Math 147 - Spring 2014
Homework 3
These problems are due on Thursday, April 24th , at the beginning of class.
1. Let A be a measure zero subset of Rk . Show that A Rl is of measure zero in Rk+l .
2. Let Z be an l-dimensional submanifold of X and let z Z.
Math 147 - Spring 2014
Homework 5
These problems are due on Tuesday, May 27th , at the beginning of class.
1. Two submanifolds N and N of M are said to intersect transversally if for each x N N
the subspaces T Nx and T Nx together generate T Mx . Note tha
Math 147 - Spring 2014
12 questions on the right denition of a manifold
These questions will be discussed in class on Thursday, May 8th. This is open book(s), open
internet, open friends. Most of the material can be found on Wikipedia, though textbooks li
Math 147 - Spring 2014
Homework 6
These problems are due on Tuesday, June 3rd , at the beginning of class.
1. The Whitney embedding theorem implies that RP2 can be embedded in R4 . Find an explicit
embedding, and be sure to prove that your map is indeed a