Instructor: Andrew Hanlon
Course on canvas.dartmouth.edu.⇗
Syllabus
| Date | Topic | References |
| M 3/31 | Why algebraic topology? Point-set review | Hatcher's notes Links to an external site., online Links to an external site. motivation Links to an external site. even on understanding straws Links to an external site., lecture notes Download lecture notes |
| W 4/2 | Categories | Chapter 1 of Riehl's Category Theory in Context Links to an external site., lecture notes Download lecture notes |
| F 4/4 | Fundamental group(oid) | §1.1, lecture notes Download lecture notes |
| M 4/7 | π1(Sn) for n>1 | §1.1, lecture notes Download lecture notes |
| W 4/9 | Covering maps and path lifting | §1.1, lecture notes Download lecture notes |
| F 4/11 | No class - moved to 4/24 X hour | |
| M 4/14 | π1(S1) and first applications | §1.1, lecture notes Download lecture notes |
| W 4/16 | Borsuk-Ulam theorem, Fundamental theorem of algebra | §1.1, lecture notes Download lecture notes |
| F 4/18 | Jordan curve theorem | Article Links to an external site. by Ryuji Maehara, lecture notes Download lecture notes |
| M 4/21 | More on JCT, deformation retracts | §0, 1.1, lecture notes Download lecture notes |
| W 4/23 | Homotopy equivalence | §0, 1.1, lecture notes Download lecture notes |
| Th 4/24 | weak Seifert-van Kampen, Free groups | §1.2, lecture notes Download lecture notes |
| F 4/25 | Seifert-van Kampen theorem | §1.2, lecture notes Download lecture notes |
| M 4/28 | Surfaces and their fundamental groups | §1.2, lecture notes Download lecture notes |
| W 4/30 | CW complexes, equivalent coverings | §0, 1.3, lecture notes Download lecture notes |
| F 5/2 | General lifting theorem | §1.3, lecture notes Download lecture notes |
| M 5/5 | Coverings correspond to subgroups | §1.3, lecture notes Download lecture notes |
| W 5/7 | Normal coverings, chain complexes | §1.3, 2.1, lecture notes Download lecture notes |
| F 5/9 | Singular homology | §2.1, lecture notes Download lecture notes |
| M 5/12 | Properties of singular homology | §2.1, 2.A, lecture notes Download lecture notes |
| W 5/14 | Homotopy invariance | §2.1, lecture notes Download lecture notes |
| F 5/16 | Barycentric subdivision | §2.1, lecture notes Download lecture notes |
| M 5/19 | Mayer Vietoris, excision, degree, and applications | §2.2, lecture notes Download lecture notes |
| W 5/21 | Cellular homology | §2.2, lecture notes Download lecture notes |
| Th 5/22 | Cellular computations | §2.2, lecture notes Download lecture notes |
| F 5/23 | No class - moved to 5/22 X-hour | |
| M 5/26 | Memorial Day - no class | |
| W 5/28 | Eilenberg-Steenrod axioms | §2.3, lecture notes Download lecture notes |
| F 5/30 | Cohomology | §3.1, lecture notes Download lecture notes |
| M 6/2 | Cup product, Künneth formula | §3.2 |
| W 6/4 | Where can you go from here? |