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Results tagged with homotopy-theory
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user 8824
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.
5
votes
Realizing $\mathcal{A}(2)//\mathcal{A}(1)$ by a finite spectrum
As pointed out by John Rognes, this answer is not correct (it misses the $Sq^4$ from the bottom class to the class in dimension $4$). Sorry for the confusion.
=========== previous answer ============ …
12
votes
Geometric interpretation of families in the stable homotopy groups of spheres
This has been a burning question for quite some time, but not much is known. Surely, people believe that the next layer (i.e. the $\beta$-family) should also admit a geometric description, although as …
- 1,554
15
votes
What are the best known results for the stable homotopy groups of spheres?
Computing $\pi_\ast(S)$ is a tedious business that to this day can only be done "by hand", i.e. by humans. The $p=2$ computation up to dimension 64 was completed by Kochman (see his SLNM book) with la …
- 1,554