More drawings by Robert Ghrist. Point-set topology, differential topology, geometric topology, symplectic topology, algebraic topology illustrated. From his (free) notes on applied homology.


  • Topology = connections between things.
  • Manifolds come in a wide variety of shapes, but they’re all tame.
  • Vector fields = arrows on a manifold.
  • Differential = linear approximation.
  • Symplectic = isotropic + antisymmetric + bilinear. (erm, not as complicated as it sounds)
  • Phase Space means these things can be conceptual rather than literal.

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