Math 443 Algebraic topology.
Fall,
2025.
Lecture notes and recordings.
This page will
give handwritten notes for each lecture as the semester progresses. It is
written in reverse chronological order, so you see the most recent
notes first. However this means that helpful links appear when a
topic is first mentioned chronologically, meaning the last time
it appears below.
Here are the
lecture notes from Fall 2024.
December 8, 2025. Today's lecrure is based on the talk I gave in Glasgow via Zoom in May, 2022. Slides and video for it can be found here. Zoom recording, which I started 20 minutes late. A video of the original lectire is available.
December 3, 2025. Limits and colimits in an infinity category. used slides shown here The Euler characteristic. Lecture notes. Zoom recording.
December 1, 2025. The definition of an infinity category. I used slides shown here .
November 19, 2025. The Kunneth theorem and the cellular chain complex. Lecture notes. Zoom recording.
November 12, 2025. End and coends. The universal coefficient theorem. Lecture notes. Zoom recording.
November 5, 2025. Introduction to homological algebra: Tor and Ext Lecture notes. Zoom recording.
October 8, 2025. The excision axiom Lecture notes. Zoom recording.
October 6, 2025. The homotopy axiom Lecture notes. Zoom recording.
October 1, 2025. Turing page. Consequences of the Eilenberg-Steenrod axioms. Lecture notes. Zoom recording.
September 29, 2025. Chain complexes and the Eilenberg-Steenrod axioms. Lecture notes.
September 24, 2025. Proving universal covering space theorem. Lecture notes. Zoom recording .
September 22, 2025. Proving the van Kampen theorem. Introduction to covering space theory. Lecture notes. Zoom recording.
September 17, 2025. Pi Day videos 1 and 2. Proving the fundamental group of S^1 is the integers. Consequence of the van Kampen theorem. Lecture notes
September 15, 2025. Fermat's last theorem page. More consequences of knowing the fundamental group of S^1: the Borsuk-Ulam theorem, the ham sandwich theorem, and the fundamental theorem of algebra. Lecture notes
September 10, 2025. Colimits, natural transformations and homotopy equivalence. The Brouwer fixed point theorem. Lecture notes
September 8, 2025. Archimedes palimpsest page. Pullbacks and limits Lecture notes
September 3, 2025. Archimedes page. Lecture notes
August 27, 2025. Dirac string video. Lecture notes
August 25, 2025. Lecture notes