Summary

Algebraic topology is a foundational topic in modern mathematics. The subject includes tools that are essential for algebra, geometry, and topology. This course is one half of a two-semester sequence that covers the subject at a graduate level. The primary text is Hatcher’s Algebraic Topology, Chapters 1 and 4.

The course primarily studies homotopy theory, including the fundamental group, higher homotopy groups, and cofiber and fiber sequences. Homology and cohomology are excluded; these topics will be covered in another semester.

A draft syllabus is available but subject to change.

Participant expectations

Each student is expected to participate fully in the course, just as if it were an in-person course at the student’s home institution. Attendance at all live meetings is required, and active participation will sometimes be expected. Students are expected to spend additional time each week engaged with the course material on their own.

A variety of formal assignments are due throughout the semester, including written homework, written exams, writing projects, and video presentations.

As a general rule, students are expected to obtain 2-3 independent study credits from their home universities for their participation in the course. At the end of the course, a letter grade A/B/C/F will be reported to each student’s home institution adviser.

Prerequisites

Students are expected to have a strong background in point-set topology and abstract algebra. See the draft syllabus for more details.

Instructors

Jack Carlisle (University of Notre Dame) is the lead instructor. Scotty Tilton (UC San Diego) is the graduate teaching assistant.

Application

Please submit the application form to apply. Applications received by December 11 will receive full consideration. Unfortunately, space is limited, and we may not be able to accept all qualified applicants. We will respond to applicants by December 18.

Schedule

The course meets on Mondays, Wednesdays, and Fridays at 11:00-11:50am eastern time, starting January 17 and ending on May 3. The week of March 11 will be a break.