General information
Instructor: Wouter van Limbeek
Office: SEO 511
Email: wouter@uic.edu
Book: John M. Lee's Introduction to Smooth Manifolds . Available for free download from the UIC Library here.
Grades: Blackboard.
Syllabus: Download.
Lectures: MWF, 12:00-12:50AM in AH 310.
Office hours: M, 11 am-12 pm and T 10-11 am.
Exams
Midterm: 2/26, in-class.
Final: will be take home. Material: Chapters 1-17 of the textbook, except the following sections:
Categories and Functors (Ch. 3), Group Actions and Equivariant Maps (Ch. 7), Time-Dependent Vector Fields and First-Order PDEs (Ch. 9), Riemannian Metrics (Ch. 13), Riemannian Volume Form (Ch. 15), Integration on Riemannian Manifolds (Ch. 16), Proof of the Mayer-Vietoris Theorem (Ch. 17).
Assignments
Due : Beginning of class on date listed.General comment: Please submit solutions offline (and stapled if consisting of multiple sheets!).
Numbers refer to problems in the textbook.
Homework 1 (due 1/17): 1-1, 1-3 (you may use Prop. A.16), 1-6, 1-7, 1-9, 1-11.
Homework 2 (due 1/24): 2-2 (see also Exs 1.8 and 1.34), 2-3, 3-1, 3-6, 3-8 (see p. 72 for definition of velocities and 3.23 for surjectivity).
Homework 3 (due 1/31): 2-7, 2-10, 2-14, 3-2, 3-4.
Homework 4 (due 2/7): 3-3, 4-1, 4-2, 4-4, 4-6, 4-8.
Homework 5 (due 2/14): 4-9, 4-10, 4-12, 5-5, 5-14, 5-15.
Homework 6 (due 2/21): 5-1, 5-6, 5-10, 5-23, 6-1.
Homework 7 (due 3/6): 6-2, 6-7 (only the part about 6.26), 8, 10, 13, 16(d). Correction: Do not do 6-13(c). It is false without assuming the image of F' is an embedded submanifold, in which case it easily follows from (b).)
Homework 8 (due 3/13): 7-2, 4 and 8-1, 4, 16, 18.
Homework 9 (due 3/27): Read Ch. 12 up to `Tensors and Tensor Fields on Manifolds' (p. 316). In addition: 8-25, 9-1(a), 9-6, 9-7, 9-16, 9-17(c).
Homework 10 (due 4/10): 10-13, 11-5, 11-7(a), 11-14(b) and (c), 11-16, 11-17, 14-1 , 14-6 (for (b), do not do the verification).
Homework 11 (due 4/17): 15-4, 15-5 (only for TM), 15-10, 15-13 (you can use the statement of 15-12), 16-3(a), 16-4, 16-5.
Homework 12 (due 4/24): 17-1, 17-4, 17-8, 17-12, 17-13.