MATH 215A Notes: Algebraic Topology

Fall 2024
By Aathreya Kadambi
Expanding on Lectures by Professor Alexander Givental and Fomenko and Fuchs

I’m taking algebraic topology by Professor Givental! The goal of the class is to cover a dense subset of Chapters 0 through 2 of Fomenko and Fuchs’s Homotopical Topology.

If you don’t know what topological spaces, they are just basic operations + classical spaces. What we will do today is classical spaces.

Flow of Stories

• Story 1: What are Classical Spaces and Groups?
• Story 2: Constructing More Spaces
• Story 3: Homotopies
• Story 4: Cell Spaces
• Story 5: Homotopy Theory of Cell Spaces
• Story 6: Fundamental Groups
• Story 7: Van Kampen Thoerem
• Story 8: Homotopy Groups