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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

3 votes

The algebro-geometrical version of K-theory

Instead of CW complexes you can also use simplicial homotopy theory (as explained in Goerss-Jardine's book of that title or Hovey's book on model categories) and define homotopy groups in the combinat …
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