344-2 - Introduction to Topology

Lectures: Monday, Wednesday, Friday 2:00pm - 2:50pm, Lunt 107
Section Meetings: Tuesdays 2:00pm - 2:50pm, Lunt 107
Course website: www.math.northwestern.edu/~tosatti/top.html

Instructor:

Valentino Tosatti
Email: tosatti@math.northwestern.edu
Office: Lunt 225

Office hours:

Tuesdays 2:00pm-3:00pm
or by appointment

Course Description:

This course is a continuation of 344-1, and is an introduction to basic algebraic topology. See the syllabus below for more detailed content information.

Textbook:

J.R. Munkres - Topology, Second Edition, Prentice Hall 2000.

Homework:

There will be written assignments which can be found below along with the due date and time. Problem sets are due on Mondays in class, except as marked below.

Grading and Final:

The class grades will be based on the homework assignments (25% total), the two midterm exams (20% each) and on the final exam (35%). The final take-home exam is due on Wednesday, June 7 at 5:00pm.

Daily Schedule:

This is a tentative syllabus and it is likely to change as the course progresses.

Date Topics Covered Remarks
Mar. 27, 29, 31 The fundamental group Homework 1
Due April 3 in class
Apr. 3, 5, 7 Covering Spaces Homework 2
Due April 10 in class
Apr. 10, 12, 14 Brouwer Fixed Point Theorem Homework 3
Due April 17 in class
Apr. 17, 19, 21 Borsuk-Ulam Theorem Homework 4
Due April 24 in class
Apr. 24, 28 Deformation Retracts
Apr. 26 First Midterm Practice Midterm
Solution of practice
Midterm with solution
May 1, 3, 5 Free Groups Homework 5
Due May 8 in class
May 8, 10, 12 Seifert-van Kampen Theorem Homework 6
Due May 15 in class
May 15, 17, 19 Universal Covering Space Homework 7
Due May 22 in class
May 22, 26 Fundamental groups of graphs
May 24 Second Midterm Practice Midterm
Solution of practice
Midterm with solution
Jun. 7 Final Take-Home Exam Due at 5pm on June 7 by email
tosatti@math.northwestern.edu