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Morse homology is a tool in differential topology and algebraic topology that studies the topology of a smooth manifold using the critical points of smooth functions defined on the manifold. It relates the topology of the manifold to the critical points of a Morse function, which is a smooth function where all critical points are non-degenerate (i.e., each critical point has a Hessian that is non-singular).

Ancestors (6)

  1. Homology theory
  2. Algebraic topology
  3. Fields of abstract algebra
  4. Fields of mathematics
  5. Mathematics
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