Skip to main content
  1. Teaching/

Topics in Differential Topology

For master’s students; Semester 1, intensive course · Graduate School of Science and Technology, Niigata University

Syllabus

Note

This course is held online via Zoom.

Textbooks

  1. Y. Hiraoka, “タンパク質構造とトポロジー” (in Japanese), Kyoritsu Shuppan

Course contents

  1. Simplicial complexes; abstract simplicial complexes; homotopy
  2. The nerve theorem, part 1
  3. The nerve theorem, part 2; simplicial-complex models of proteins
  4. Groups and rings
  5. Modules over rings
  6. Homology groups, part 1
  7. Homology groups, part 2
  8. Homology groups of proteins; $\mathbb{Z}/2\mathbb{Z}\lbrack x \rbrack$-modules
  9. Persistent homology groups, part 1
  10. Persistent homology groups, part 2; persistent homology groups of proteins