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Results tagged with homotopy-theory
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user 108901
Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
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When are two kinds of weak equivalence 'the same'?
First, an observation: Here are two examples of when different notions of weak equivalence in a category turn out to be the "same":
(Whitehead's Theorem) Two CW complexes are homotopy equivalent if …
- 55.9k
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Notation: Why Ω for the based loop functor?
This is just a question about notation - probably useless, but it's always baffled me:
Why was $\Omega$ chosen to denote the based loop functor?
I once heard someone speculate: "It's because $\Omega …
- 113