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Results tagged with homotopy-theory
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user 5690
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.
48
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6
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Why the "W" in CGWH (compactly generated weakly Hausdorff spaces)?
In his 1967 paper A convenient category of topological spaces,
Norman Steenrod introduced the category CGH of compactly generated Hausdorff spaces
as a good replacement of the category Top topological …
- 43.2k
36
votes
0
answers
1k
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Functor that maps to both $KO^n$ and $KO^{-n}$
(my question is also meaningful for complex K-theory, but since Kn(X) is always isomorphic to K-n(X), it's less interesting)
I start by recalling the analytic definition of KO-theory:
The following …
- 43.2k
25
votes
2
answers
960
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Is super-vector spaces a "universal central extension" of vector spaces?
Is there some sense in which the category $sVect$ of super-vector spaces is the "maximal non-trivial extension" of $Vect$ as a symmetric monoidal category?
Is the $\mathbb Z/2$ that shows up in the d …
- 43.2k
19
votes
3
answers
1k
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Are Chern classes well defined up to contractible choice?
The Chern classes are, by definition, cohomology classes. And
cocycle representatives of the Chern classes are not unique.
But it might be the case that cocycle representatives of the Chern classes ar …
- 43.2k
36
votes
3
answers
2k
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Defining $SU(n)$ in HoTT
From a recent answer by Mike Shulman, I read:
"HoTT is (among other things) a foundational theory, on roughly the same ontological level as ZFC, whose basic objects can be regarded as $\infty$-gro …
- 43.2k