Math 8302
Spring 2019

Location and time: Vincent Hall 209, MWF 1:25pm-2:15pm

Text: Topology: A Geometric Approach by Terry Lawson.
Text: Differential Forms in Algebraic Topology by R. Bott and L. Tu.
Link to download the book
http://users.metu.edu.tr/serge/courses/422-2014/supplementary/TGeometric.pdf


Lecturer: Tian-Jun Li, Vincent Hall 260, (612) 625-2036
Email: lixxx248@umn.edu
URL: http://www.math.umn.edu/~lixxx248
Office hours: 10:30-11:30 on Fridays, 11-12 on Mondays.


Course Content

Sections 5, 6, 7, 12, 15, 16, 17 in Chapter 6 and sections 5, 6, 7 in Chapter 3 of the book by Lawson.
Chapter I, Chapter II and Section 15 of the book by Bott-Tu. Gauss-Bonnet Theorem, Frobenius Theorem.
Homework
There will be 7 or 8 homework problem sets.

Homework 1, due Feb 8 (Friday).
Exercises in Chapter 6: 5.12, 6.6, 6.7, 6.11, 16.10, 17.15, 7.3, 12.3, 12.19, 12.20
This week's Friday office hour: 11-12.       
Solutions to Hw1


Homework 2, due Feb 18 (Monday).
Exercises in Chapter 6: 15.5, 15.12, 15.14.
Exercises in Chapter 3: 5.5, 6.1, 7.1, 7.8, 7.13, 6.10       
Solutions to Hw2


Homework 3, due March 4 (Monday).
From the book of Bott-Tu:
Exercises 2.1.1, 3.6, 4.3.1, 4.5, 4.8
      
Solutions to Hw3 (by Bruno Poggi)


Homework 4, due March 25 (Monday).
From the book of Bott-Tu:
Exercises 5.12, 5.16, 6.2, 6.10, 6.14, 6.20
      
Solutions to Hw4 (by Bruno Poggi)


Homework 5, due April 8 (Monday).
From the book of Bott-Tu, Chapter 6:
Exercises 32, 36, 43, 44, 45, 46
Special office hour: Friday (4/4), 2:30-3:30.
      
Solutions to Hw5 (by Lilly Webster)

Note: For 6.45, the integral of the Euler class should be -1.

Solutions to Exercise 6.45 (by Bruno Poggi)


Tests.
There are two in class tests and a take home final.
Test 1 on Wednesday, 2/27. It covers the sections of HW1 and HW2.
Test 2 on Monday, 4/22. It covers Sections 1-6 of Bott-Tu.

Take home final problems, due Friday, 5/10.

Exercises 8.4, 11.19, 11.26, more to come.
Grading
Each test accounts for %15 and the take home final accounts for %20, and homework accounts for %50.