John Milnor's Exotic 7-Spheres скачать в хорошем качестве

John Milnor's Exotic 7-Spheres

Exotic spheres are manifolds that are topologically the same as the usual n-sphere but have a different smooth structure. Milnor discovered the first examples in 1956 by constructing S3-bundles over S4, showing that the 7-sphere has several distinct smooth structures. This is the first-known counterexample of smooth Poincaré conjecture. The original construction is from John Milnor’s “On Manifolds Homeomorphic to the 7-Sphere.” Niles Johnson’s original video(   • Visualizing Seven-Manifolds  ), which inspired part of the visualization. I noticed quite a few mistakes, and I’ll post the corrections in the description or comments soon. This project was created using Three.js, Manim, Blender, Audacity, and Kdenlive. Music Used in This Video: Xylo-Ziko — CC BY-NC-SA 4.0 "Droplets" by Xylo-Ziko "Sway" by Xylo-Ziko "Patina" by Xylo-Ziko "Parched" by Xylo-Ziko Pixabay Music — Pixabay Content License "Science and Research (Inspiring Futuristic Technology)" by DIMMYSAD "Space Ambient" by DELOSound "Beyond Infinity" by BlenderTimer #maths #topology #visualization #geometry #some4