Timeline for What is the first interesting matric Toda bracket in the stable homotopy of the sphere?
Current License: CC BY-SA 3.0
5 events
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| Jun 11, 2017 at 9:48 | comment | added | Achim Krause | I'm afraid I don't know a nice reference for matric Toda brackets, but you can certainly introduce them as usual smash Toda brackets between spectra of the form $\bigvee_{i,j} S^{d_{ij}}$, using multiplication maps that look like the usual multiplication rules for matrices. After my edit, all the degrees are consistent in the example above. Alternatively (but that's less consistent with the argument in the post), describe them as composition Toda brackets between spectra of the form $\bigvee_i S^{d_i}$. | |
| Jun 11, 2017 at 9:42 | comment | added | Achim Krause | Looking back at this 3-year old post, I'm not actually sure whether inhomogeneous Toda brackets make sense, but noticed that setting the lower right entry to 0 makes this into perfectly fine homogeneous matric Toda brackets, so I edited it. | |
| Jun 11, 2017 at 9:40 | history | edited | Achim Krause | CC BY-SA 3.0 |
Changed the original description of the Toda bracket, which was inhomogeneous, to one that is homogeneous.
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| May 29, 2017 at 16:28 | comment | added | Dylan Wilson | Do you know of a reference that discusses these "mixed degree" Toda brackets? The literature seems to require some compatibility between the degrees in the matrix entries which isn't satisfied here. Actually- any readable references at all for matric Toda brackets would be nice. The "literature" barely exists. | |
| Mar 9, 2014 at 6:11 | history | answered | Achim Krause | CC BY-SA 3.0 |