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Results tagged with homotopy-theory
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user 1631
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
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A conceptual proof that local fibrations over paracompact spaces are global fibrations?
The following runs out of steam towards the end; I may also be making important mistakes, so be on your guard --- but that's half the fun! Anyways, it was too long for a comment.
Choose a locally-fi …
- 19.3k
12
votes
4
answers
2k
views
The most general context of Mather's Cube Theorems
Quite simply, I'd like to know what is the broadest or most natural context in which either (or both) of Mather's cube theorems hold. If you like, this may mean any of
What properties of $Top$ or $T …
- 17.8k
13
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0
answers
781
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What's so difficult about $\pi_{15}(SO)$?
Regarding the table of $SO(n)$s-of-origin in Davis+Mahowald (if you can get MathSciNet), is there a good reason that it should take longer for $\pi_{15}(SO)$ to be representable than $\pi_{19}(SO)$, w …
- 1,987
12
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Accepted
Geometric meaning of torsion in homotopy groups
Well, the silly answer is that $f:\mathbb{S}^k\to X$ represents a torsion element of order $p$ if $p \cdot f:\mathbb{S}^k\to X$ extends along $\mathbb{S}^k \hookrightarrow D^{k+1}$ to a map $\varphi: …
- 1,987