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Results tagged with homotopy-theory
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user 343
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.
2
votes
Killing the torsion in homotopy
It might go without saying, but there is a procedure for non-simply connected spaces if you're killing a perfect torsion subgroup. It's just Quillen's plus construction used in the construction of alg …
- 1,422
2
votes
2
answers
366
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Classifying space of a crossed complex
Brown defines the classifying space of a crossed complex in the following way.
Given a filtration X* of a space X, define the fundamental crossed complex by:
C_0 = X_0, C_1=\pi(X_1,X_0) (the fundamen …
- 1,422
3
votes
1
answer
223
views
Explicit classifying spaces for crossed complexes
I'm trying to understand the topology behind a certain group which fits into a truncated crossed complex, so I've been trying to understand Brown's construction of the classifying space of a crossed c …
- 1,422
7
votes
3
answers
2k
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Crossed module structure on homotopy groups
A crossed module is a pair of groups $C$ and $G$, an action of $G$ on $C$, and a homomorphism $\partial: C \to G$ that satisfy
$\partial(g\cdot c)=g(\partial c)g^{-1}$, and
$cc'c^{-1}=(\partial c) …
- 1,422
7
votes
References for homotopy colimit
A good (if kind of old) reference is Vogt's "Homotopy Limits and Colimits". I can't find a free reference for it, but if you can't access it, I could email a pdf (if that's allowed here).
Also, in th …
- 1,422