Exam 2: Math 7350 Spring 2013
Professor William Ott
Problem 1. (Cartan lemma) Let M be a smooth n-manifold and let ( 1 , . . . , k ) be an ordered k -tuple of
smooth 1-forms such that ( 1 |p , . . . ,
UH - Math 7350 - Dr. Heier - Spring 2016
HW 1
Due 02/17/12, at the beginning of class.
Use regular sheets of paper, stapled together.
Dont forget to write your name on page 1.
1. (1 point) Give an exa
UH - Math 7350 - Dr. Heier - Spring 2016
HW 4
Due Wednesday, 04/20, at the beginning of class.
Use regular sheets of paper, stapled together.
Dont forget to write your name on page 1.
1. (2 points) In
UH - Math 7350 - Dr. Heier - Spring 2016
HW 2
Due Wednesday, 03/09, at the beginning of class.
Use regular sheets of paper, stapled together.
Dont forget to write your name on page 1.
1. (2 points) Le
UH - Math 7350 - Dr. Heier - Spring 2016
HW 3
Due 03/23/16, at the beginning of class.
Use regular sheets of paper, stapled together.
Dont forget to write your name on page 1.
1. (2 points) Problem 4-
Justin Le
Professor Sara Rolater
English 1304
6 November 2016
Fluorides Consequences
Looking at one of Americas most controversial topics is the addition of fluoride into
Americas water supply. I want
Assignment 1: Math 7350 Spring 2013
Professor William Ott
Problem 1. Let X = (x, y ) R2 : y = 1 or y = 1 and let M be the quotient space obtained from X
by identifying (x, 1) with (x, 1) for all x = 0
Assignment 2: Math 7350 Spring 2013
Professor William Ott
Problem 1. Dene F : Rn RPn by F (x1 , . . . , xn ) = [x1 , . . . , xn , 1]. Show that F is a dieomorphism
onto an open, dense subset of RPn .
Assignment 3: Math 7350 Spring 2013
Professor William Ott
Problem 1. Consider the map : R4 R2 dened by
(x, y, s, t) = (x2 + y, x2 + y 2 + s2 + t2 + y ).
(a) Show that (0, 1) is a regular value of .
(b
Assignment 4: Math 7350 Spring 2013
Professor William Ott
Problem 1. Let M be a connected smooth manifold. Prove that for every p, q M , there exists a
dieomorphism F : M M such that F (p) = q . (This
Exam 1: Math 7350 Spring 2013
Professor William Ott
Problem 1. Let G be a Lie group. Prove that the multiplication map m : G G G is a smooth
submersion. Hint: use local sections.
Problem 2. Let G be a
UH - Math 7350 - Dr. Heier - Spring 2016
HW 5
Due no later than Wednesday, May 04, 3pm, at my office PGH 666
(if I am not in, please slide your solution under my office door)
or by email to [email protected]