Instructor: Dr. Károly Böröczky

Text: Allen Hatcher: Algebraic Topology, Chapters 0 and 2, handouts

Prerequisite: Some introductory topology (say a real analysis class), and some introductory algebra  (essentially the notion of Abelian group)

Course description: We start with a short course on the point set topology, which is an essential part of modern analysis, to be ready for algebraic topology, which is one of the most dramatic topic of modern geometry. Level depends on the background of the class.

Topics:

• Notion of homotopy and homotopy type
• Simplicial complexes and Cell complexes
• Homotopy extension property
• Simplicial homology
• Singular homology
• Exact sequences and Excision
• Degree
• Axioms for Homology Theory
• Mayer Vietoris Sequences
• Brouwer fixed point theorem
• No wind theorem
• Borsuk-Ulam theorem
• Invariance of domains