Synopsis:

• This course is a continuation of Math 551. The main focus of the course will be on the fundamental group and the associated theory of covering spaces. We will cover the Seifert-van Kampen theorem, which is one of the main tools for computing fundamental groups, as well as the classification of surfaces. The last part of the course will be devoted to homology.

Texts:

• Intro to Topological Manifolds, John M. Lee (available online)
• Algebraic Topology, Allen Hatcher (available online)

Test dates (estimate):

• Test 1: Friday, Feb. 16,
• Test 2: Wednesday, Mar. 28,

Final exam: Thursday, May 3, 8:00-10:00 AM

Homework: Homework exercises will be assigned to complement the material in the lectures and collected every Friday. You are strongly encouraged to work in groups on the homework, but you must write up your solutions independently. There will be no homework due the week of an exam.

Grading policy: The breakup will be: Homework - 25%, Midterm I - 25%, Midterm II - 25% , Final exam - 25%.