An Introduction to Algebraic Topology
Posted by John Baez
This quarter, besides my seminars on Quantization and Cohomology and Classical vs. Quantum Computation, I’m also teaching the graduate qualifier course on algebraic topology. While a bit elementary for some Café regulars, it might be fun for other folks:
- John Baez, Mike Stay and Christopher Walker, Algebraic Topology.
The lectures are by John Baez, except for classes 2-4, which were taught by Derek Wise. The lecture notes are by Mike Stay, and until the course is finished in mid-March, his notes may be more up-to-date. The answers to homework problems are by Christopher Walker. The course used this book:
- James Munkres, Topology, 2nd edition, Prentice Hall, 1999.
So, theorem numbers match those in this book whenever possible, and it’s best to read these notes along with the book. But, we deviate from Munkres at various points, and also skip many sections. We place more emphasis on concepts from category theory.
But, the star of the show is $\pi_1$ — the fundamental group!
Re: An Introduction to Algebraic Topology
I had a meeting this week, together with two emeriti at my university, with concerned teachers at the local mathematics-profiled secondary school. They have a handfull of school kids who simply are beyond the teacher’s capacity to handle satisfactory, and so wanted us to render some backup.
I got two very ambitious 9th-graders; and am toying with the idea of nudging them into algebraic topology over the Euler characteristic (which they probably know in the classical case).
One idea that occurred to me there was whether or not the fundamental groupoid may even be easier to start with than the fundamental group, if only you introduce it the right way. Thoughts?