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Results tagged with homotopy-theory
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user 148793
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.
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Give a null-homotopy of $2\eta :S^4\to S^3$ in coordinates
where $\eta$ is the suspension of the hopf fibration.
When I say "in coordinates" I mean that $2\eta$ comes from choosing an explicit representation of $\eta :S^3\to S^2$, suspending it, composing wi …
- 348
4
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1
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Reference request for a calculation of a Toda-bracket of spheres
For example a calculation of $S^5\overset{\eta}{\to} S^4\overset{2}{\to} S^4\overset{\eta}{\to} S^3$.
I know this exists in Toda's book.
However, I'm looking for a fairly elementary proof that is ea …
- 348
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What is known about homotopy groups of spheres?
I'm looking for a list/table/survey of what is known (and what is not known) about homotopy groups of spheres, for example: which are known, which are known stably, which are known primally, non-$0$ …