Term 2, Mon. Period 3 & Thu. Period 4 · Faculty of Science, Niigata University
Note
Held on Mon. Period 3 & Thu. Period 4.
Textbooks
- K. Komiya, “位相幾何入門” (in Japanese), Shokabo
Main references
- I. Tamura, “トポロジー” (in Japanese), Iwanami Zensho
Recommended reading
- Y. Hiraoka, “タンパク質構造とトポロジー” (in Japanese), Kyoritsu Shuppan
Course contents
- Topological spaces
- Quotient spaces; closed surfaces and connected sums
- Classification of closed surfaces
- Simplices and simplicial complexes
- Skeletons and polyhedra; group theory, part 1
- Group theory, part 2; oriented simplices
- Chain groups and homology groups
- Midterm exam
- Computing homology groups; simplicial maps
- Chain homomorphisms; homology groups of polyhedra, part 1 (definitions); homotopy
- Homology groups of polyhedra, part 2 (homotopy invariance)
- Euler numbers; homology groups and homomorphisms
- The Mayer-Vietoris exact sequence
- Homology groups of closed surfaces
- Persistent homology groups and protein structures
- End-of-term exam and summary