Transverse circles in flag manifolds of split real Lie groups are locally maximally transverse exactly for the pairs listed in Table 1, and new spinor-constructed transverse spheres of arbitrary dimension are proven maximally transverse via the Atiyah-Bott-Shapiro isomorphism.
Baez and John Huerta
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Transverse Spheres in Flag Manifolds
Transverse circles in flag manifolds of split real Lie groups are locally maximally transverse exactly for the pairs listed in Table 1, and new spinor-constructed transverse spheres of arbitrary dimension are proven maximally transverse via the Atiyah-Bott-Shapiro isomorphism.