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Results tagged with homotopy-theory
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user 6023
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
Is there an interesting definition of a category of test categories?
I'm not sure what “interesting” means in this context. It's probably too much to demand that morphisms between $\widehat{C_1} = \mathbf{Set}^{{C_1}^{\mathrm{Op}}}$ and $\widehat{C_2} = \mathbf{Set}^{ …
- 498
4
votes
Dyer-Lashof based spectral sequence for homotopy classes of maps between infinite loop space...
I'm not sure if this is what you want, but Haynes Miller constructs a spectral sequence computing the homology of a connective spectrum $E$ from the homology of $E_0$ as a Hopf algebra over the Dyer-L …
- 498
12
votes
1
answer
633
views
The semidihedral group of order 16 and ko
Let $\mathcal{A}(1)$ denote the subalgebra of the $\mathrm{mod}\ 2$ Steenrod algebra generated by $\mathrm{Sq}^1$ and $\mathrm{Sq}^2$.
The cohomology with $\mathbf{F}_2$ coefficients of the semidihedr …
- 498