## 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.