Timeline for Relationship between induced maps at homotopy groups level for maps $f:S^2\to S^2$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Oct 17, 2019 at 21:17 | comment | added | Noah Snyder | A fun consequence is that stably there's a commutative product which agrees with both of these compositions, so stably $2 \eta = \eta 4$ and hence $2 \eta$ is trivial stably. | |
| Dec 9, 2018 at 16:10 | vote | accept | X1921 | ||
| Dec 3, 2018 at 12:53 | comment | added | Bertram Arnold | One can also directly see this from the description of the Hopf invariant in terms of the cohomology ring of the mapping cone: If $f:S^3\to S^2$ and $g:S^2\to S^2$ are any two maps, there is an induced map $C_f\to C_{g\circ f}$ which is the identity on $H^4$ and multiplication by deg$(g)$ on $H^2$ using the obvious generators of these groups. The statement then follows from naturality of the cup product. | |
| Dec 3, 2018 at 12:36 | history | answered | Neil Strickland | CC BY-SA 4.0 |