MATH 622, Differential Geometry I,
Spring 14
Syllabus
Homework 1 (from the first edition of Lee) Due Thursday Jan 23: Lee-p.28-29 Problems 1-4,
1-5, 1-6 (here the standard smooth structure on a circle is as in
example 1.20, p.20) ; p. 57-58 Problems 2-3, 2-4.
For those who have the second edition of the textbook,
unfortunately the problems there are different (or have different
numbers) from the first edition. From the first chapter you should do
1-7 and 1-8 from pages 30-31 there (corresponds to 1-5 and 1-6 of
the first edition). There is no exercize 1-4 of the first edition in
the second edition. Therefore take it from here. From the second chapter you should do 2-5 and 2-6 (corresponds to 2-3 and 2-4 of the first edition.
Homework 2 (from the
first edition of Lee) Due Tuesday Feb. 4: Lee p. 66 Exercize 3,2; pp.
78-79 3-1, 3-2, 3-3, 3-5; pp 100-101, 4-1, 4-5 (a), (c)
For those who have the second edition of the textbook: Lee p.56 Exercize 3.7; problems 3-1, 3-2, 3-3, and 3-5 from the first edition here
(note that in your edition 3-1 has a different formulation than in the
first edition, 3-2 is the same, other exercises are missing); p.
75 3-4 (in your edition this problem corresponds to 4-1 of
page 100 in the first edition);
peoblem 4-5 (a), (c) from here.
Homework 3 (from the
first edition of Lee) Due Thursday Feb. 13: p. 79 problem 3-6, p. 92
Exercise 4.6; p. 101-102 problems 4-10, 4-11, 4-12, 4-14, 4-15.
For those who have the second edition of the textbook:
p. 171 problem 7.2 (corresponds t0 p. 79 problem 3-6 of the first
edition) p.188 Exercise 8.29 (corresponds to p. 92 Exercise 4.6
of the first edition), p. 201-202 problems 8-16, 8-19, 8-20, 8-21
(corresponds to 4-11, 4-12, 4-14, 4-15 of the first edition
respectively) . I did not find the analog of problem 4-10 of the first
edition so please find it here.
Homework 4 (from the
first edition of Lee) Due Tuesday, Feb 25: p. 151-152 problems 6-4,
6-5, 6-2 (a) (for the definition of the bundle map see p. 115), 6-3
(for the definition of a trivial vectorbundle see p. 104-105); p.
287 problem 11-8 (here Sigma^k stand for the space of symmetric
covariant k-tensors), p 319-321 problems 12-3, 12-4, 12-5.
For those who have the second edition of the textbook: p. 301-302 problems 11-9, 11-10 (corresponds to 6-4, 6-5 of the first edition) , 11-8 (a) (corresponds
to 6-2(a) of the first edition, for the definition of the bundle
homomorphism (map) see p. 261), 11-5 )corresponds to 6-3 of the first
edition, for the definition of the trivial vector bundle see p. 250);
p. 325 problem 12-5 (corresponds to 11-8 in the first edition); p. 373
problem 14-1 (corresponds to 12-3 of the first edition). There is no
exact analogs of problems 12-4 and 12-5 of the first edition, so please
find them here
Homewrok 5 (from the
first edition of Lee) Due Thursday, March 6: p.320 problems 12-6.
12-7; p. 171 problems 7-3, 7-5 (in the last problem M must be
nonempty)
For those who have the second edition of the textbook: p. 375 problems 14-6, 14-7; p. 96 problems 4-4, 4-6.
Homewrok 6 (from the
first edition of Lee) Due Tuesday, March 25, pp. 201-203 problems 8-1, 8-2, 8-13, 8-14, 8-16, 8-18.
For those who have the second edition of the textbook: p.
123-124 problems 5-1, 5-7, 5-11, 5-19 (correponds to
8-1, 8-2, 8-13, 8-14), I did not find the analogs of problem 8-16 and
8-18 , so please find them here
Midterm will take place on Wednesday, April 2, in Blocker 624, from 7-9 p.m.
More information about the midterm was sent to you by email.
Homewrok 7 (from the
first edition of Lee) Due Tuesday, April 8, p. 515-516 problems 19-2,
19-3, 19-5 (for the definition of exact form see p. 310), 19-6, 19-7.
For those who have the second edition of the textbook: p
512-513 proble,s 19-2 (the same number as in the first edition), 19-3 (
corresponds to 19-5 in the first edition; for the definition of exact
form see p. 367), 19-4, 19-5 (correspond to 19-6, 19-7 in the first
edition), I did not find the analogs of problem 19-3 of the first
edition, so please find it here
Homework 8 Due Thursday, April
24, From chapter 1 of ''Cartam for Beginners'' (distributed by
email and in class)- p. 41 Exercise 2.2.2 items 1, 2, 3;
Exercises 1 b) c) and 3 from the following pages; the following exercise (the latter is a bonus question of 40 points and it is similar to Exercise 2.3.1 items 2,3,5 of ''Cartan for Beginners'')
Homework 9 (can be submitted as an extra credit till Monday, May 5 to my office, swipe under the door if I am not there; recommended to try because the material is a part of the final) Exercises 5 and 7 from p. 97 of the following pages; Exercises 2,3,4,5 from the following pages