Math 443 Algebraic topology.
Fall, 2024.
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.

Lecture notes and recordings for this semester:

• December 4, 2024. Eilenberg-Mac Lane sapces II. Lecture notes Zoom recording

• December 2, 2024. Eilenberg-Mac Lane spaces. Lecture notes Zoom recording

• November 25, 2024. Cup products and the Serre spectral sequence. Lecture notes Zoom recording

• November 20, 2024. Introduction to spectra. Lecture notes Zoom recording

• November 18, 2024. Sophie Germain page The Euler characteristic theorem. Lecture notes Zoom recording

• November 13, 2024. The Cartesian product of CW complexes and the Euler characteristic. Lecture notes Zoom recording

• November 11, 2024. The Dold-Kan correspondence and the cellular chain complex. Lecture notes Partial Zoom recording

• November 6, 2024. James Iler lectured on model categories today. The source for this material is Dwyer and Spalinksi's 1995 paper Homotopy theories and model categories. More material can be found Chapter 4 of the purple book.

• November 4, 2024. The universal coofficient theorem. Lecture notes Zoom recording

• November 1, 2024. Projective resolutions, Tor and Ext. Lecture notes Zoom recording

• November 1, 2024. Projective resolutions, Tor and Ext. Lecture notes Zoom recording

• October 30, 2024. Limits and colimits in an infinity category. Lecture notes Example 5.8.5. Zoom recording

• October 28, 2024. What is an infinity category? Part III. Corrected slides Lecture notes For the examples of homotopy limits and colimits, see the purple book Example 5.8.5. Zoom recording

• October 23, 2024. What is an infinity category? Part

  2. Corrected slides Lecture notes Zoom recording 1Zoom recording 2

• October 21, 2024. What is an infinity category? Part I. Slides Printed version Zoom recording The horn typo has been corrected in both the slides and the paper.

• October 16, 2024. Barycentric subdivision, the 5-lemma and the excision axiom. Lecture notes Zoom recording

• October 9, 2024. The singular chain complex and the homotopy axiom. Lecture notes

• October 7, 2024. Luke lectured on simplicial sets. No notes or recording available.

• October 2, 2024. Computing with the Eilenberg-Steenrod axioms. The projector was broken, so there are no notes or recording. Lecture notes from 2023 Lecture notes from 2022 Zoom recording from 2022.

• September 30, 2024. Chain complexes. Lecture notes Zoom recording

• September 25, 2024. Boy surface video The universal covering theorem. Lecture notes Zoom recording

• September 23, 2024. Covering space theory. The projector was not working, so no notes or Zoom recording were made. Similar materail was covered on 9/29/23 and 10/2/23.

• September 18, 2024. Alan Turing page The Van Kampen theorem. Lecture notes Zoom recording

• September 16, 2024. The fundamental group of the circle. Lecture notes No Zoom recording available.

• September 11, 2024. Brouwer fixed point, Borsuk-Ulam and Ham Sandwich theorems. Lecture notes Zoom recording

• September 9, 2024. Limits and colimits. Lecture notes Zoom recording

• September 4, 2024. Dirac string video. Pullbacks and pushouts. Lecture notes Zoom recording

• August 28, 2024. Functors. Lecture notes No Zoom recording available.

• August 26, 2024. The coffee cup trick and the fundamental group. Lecture notes A Lecture notes BZoom recording AZoom recording B