代数的トポロジー(代数的位相幾何学)のオンライン授業を,Youtube動画で。ホモロジーの入門
「代数的トポロジー」を学ぶためのオンライン講義の動画。
ニューサウスウェールズ大の,幾何の授業。
前半
- 1. AlgTop0: Introduction to Algebraic Topology
- 2. AlgTop1: One-dimensional objects
- 3. AlgTop2: Homeomorphism and the group structure on a circle
- 4. AlgTop3: Two-dimensional surfaces: the sphere
- 5. AlgTop4: More on the sphere
- 6. AlgTop5: Two-dimensional objects- the torus and genus
- 7. AlgTop6: Non-orientable surfaces---the Mobius band
- 8. AlgTop7: The Klein bottle and projective plane
- 9. AlgTop8: Polyhedra and Euler's formula
- 10. AlgTop9: Applications of Euler's formula and graphs
- 11. AlgTop10: More on graphs and Euler's formula
- 12. AlgTop11: Rational curvature, winding and turning
- 13. AlgTop12: Duality for polygons and the Fundamental Theorem of Algebra
後半
- 14. AlgTop13: More applications of winding numbers
- 15. AlgTop14: The Ham Sandwich theorem and the continuum
- 16. AlgTop15: Rational curvature of a polytope
- 17. AlgTop16: Rational curvature of polytopes and the Euler number
- 18. AlgTop17: Classification of combinatorial surfaces I
- 19. AlgTop18: Classification of combinatorial surfaces II
- 20. AlgTop19: An algebraic ZIP proof
- 21. AlgTop20: The geometry of surfaces
- 22. AlgTop21: The two-holed torus and 3-crosscaps surface
- 23. AlgTop22: Knots and surfaces I
- 24. AlgTop23: Knots and surfaces II
- 25. AlgTop24: The fundamental group
- 26. AlgTop25: More on the fundamental group