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I am recently come into the world of algebraic topology and find it a fascinating place with lots of beautiful constructions that challenge one's intuition. Also, understanding these constructions are very helpful for appreciate the theory underneath. So I would like to invite you to share those examples in AT that you think is both beautiful and enlightening.

Following is what comes to my mind at first place:

  • Sphere eversion
  • Poincaré's homology sphere (motivate the study of Poincaré conjecture and homotopy group)
  • Hopf fibration (motivate the study of homotopy groups of n-spheres)
  • Space-filling curve (motivate the study of dimension)
  • Dunce hat
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