Syllabus

A PDF version of this syllabus is available here.

Lectures

Instructor

Prerequisites

A large part of this course will depend only on the material covered in MTH 428/528 (CW complexes, the fundamental group, covering spaces). Later, we will also use homology and cohomology to the extent covered in MTH 628.

Learning outcomes

The goal of this course is to introduce some more standard material in homotopy theory:

• Higher homotopy groups
• Excision and Freudenthal suspension theorem
• Eilenberg-MacLane spaces
• Fibrations and fiber bundles
• Cofibrations
• Weak equivalences
• CW approximation
• Hurewicz theorem
• Serre spectral sequence

Textbook

This course will not follow closely any specific textbook, but there are several good texts that cover this material. For example:

• Allen Hatcher, Algebraic Topology, Cambridge University Press 2001
• Tammo tom Dieck, Algebraic Topology, European Mathematical Society 2008

Homework

Optional homework problems will be assigned periodically.

Weekly digests

Each week you will be asked to submit a short (a few sentences long) writeup on your study from the previous week. For example, you can write:

• what topics you have found interesting (or boring)
• what topics you have found difficult (or easy)
• how you feel about the course
• anything else you want to share.

You will be also asked to submit a question (or questions) that you would like to see discussed during a class meeting.

Exams

There will be no exams in this course.