notes

Lecture notes and Zoom recordings for Math 443, Fall 2022, in

reverse chronological order.

• Notes from Fall 2021

• December 16, 2022. Cup products and clock problems. Lecture notes. No Zoom redoring available.

• December 15, 2022. G-CW complexes and real projective spaces. Lecture notes. Zoom recording.

• December 14, 2022. The Euler characteristic and Platonic solids. G-CW complexes. Lecture notes. Zoom recording.

• December 12, 2022. The product CW structure and the Euler chacteristic. Lecture notes. Zoom recording.

• December 7, 2022. CW-complexes and the cellular chain complex. Lecture notes. Zoom recording.

• December 5, 2022. New Horizons Pluto flyby video. The universal coeffciisnt theorem. Lecture notes. Zoom recording.

• November 30, 2022. More about projective resolutions. Lecture notes. The Zoom recording is in two parts due to a computer crash. Part 1. Part 2.

• November 28, 2022. Sophie Germain page. Projective modules and resolutions. Lecture notes. Zoom recording.

• November 21, 2022. Barycentric subdivision and th eproof of the excision axiom. Lecture notes. Zoom recording. Unfortuntely I forgot share the screen, but if you looks at the elcture notes while listeing to the recording, you should be able to make sense of it.

• November 16, 2022. The homotopy and excision axioms. Lecture notes. Zoom recording.

• November 14, 2022. The homology of the n-sphere and the Mayer-Vietoris sequence. Lecture notes. Zoom recording.

• November 9, 2022. Simplicial sets: geometric realizations and chain complexes. The singular simplicial set and singular homology of a topological space. Lecture notes.

• November 7, 2022. Source: Section 3.4A of the purple book Prepublication draft of the purple book. Simplicial sets as functors. Lecture notes. First Zoom recording, 48 minutes. Second Zoom recording (after my computer crashed, 16 minutes.

• November 2, 2022. Nathaneal Grand lectured on simplicial sets. No notes or recording available.

• October 31, 2022. Chain complexes: the long exact sequence in homology and chain homotopy. Lecture notes.

• October 26, 2022. Fermat/Wiles video. Fermat’s Last Theorem page The proof ofthe universal covering theorem, and introduction to homology. Lecture notes. Zoom recording.

• October 24, 2022: Mandelbrot set zoom video Mandelbrot page with link to video about the Mandelbrot set. Covering spaces. Lecture notes. Zoom recording.

• October 12, 2022: Sugar plum genus 2 video More examples and the proof of the van Kampen Theorem. Lecture notes.

• October 5, 2022: Proofs of the Borsuk-Ulam theorem revsited, free groups and the Van Kampen Theorem. Lecture notes.Zoom recording.

• October 3, 2022: Proofs of the Borsuk-Ulam and Ham Sanwich Theorems. Staement of the Van Kampen Theorem. Lecture notes.Zoom recording.

• September 28, 2022: The fundamental group of the circle and its applications. Lecture notes.Zoom recording.

• September 26, 2022: Adjoint functors. Toward the fundamental group of the circle. Lecture notes.

• September 21, 2022: More about limits and colimits. Lecture notes. Zoom recording starting a few minutes late.

• September 19, 2022: Pushouts and colimits. In this class we had both a projector malfunction and a fire drill. Lecture notes.

• September 14, 2022: Archimedes Palimpsest page. CW-complexes and pushouts. Hopf fibration page. Lecture notes. Zoom recording.

• September 12, 2022: Archimedes page. Introduction to category theory. Lecture notes.

  September 7, 2022: Dirac string video. Higher homotopy groups and homotopy equivalence. Lecture notes. Zoom recording.

• August 31, 2022: The belt and coffee cup tricks. Lecture notes. No Zoom recording due to wifi breakdown.