The low degrees in the Whitehead tower of the orthogonal group are closely linked to the physics of branes appearing in string theory/M-theory. Accordingly the low stages are called
fivebrane group string group spin group special orthogonal group orthogonal group
To which extent and in which sense this matching with brane physics continues is not entirely clear. Hisham Sati gives arguments that co-killing the next integer homotopy group corresponds to the M9-brane. Therefore one might call the corresponding stage in the Whitehead tower the ninebrane group. This suggestion appeared in (Sati-Schreiber-Stasheff 08)
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Whitehead tower of orthogonal group | orientation | spin group | string group | fivebrane group | ninebrane group | |||||||||||||
higher versions | special orthogonal group | spin group | string 2-group | fivebrane 6-group | ninebrane 10-group | |||||||||||||
homotopy groups of stable orthogonal group | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||||||||
stable homotopy groups of spheres | 0 | 0 | 0 | |||||||||||||||
image of J-homomorphism | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Last revised on May 27, 2022 at 02:52:10. See the history of this page for a list of all contributions to it.