The space of almost complex 2-spheres in the 6-sphere

Fernández, Luis

doi:10.1090/S0002-9947-2014-06070-4

The space of almost complex 2-spheres in the 6-sphere
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Trans. Amer. Math. Soc. 367 (2015), 2437-2458 Request permission

Abstract:

The complex dimension of the space of linearly full almost complex 2-spheres of area $4\pi d$ in the round 6-sphere is calculated to be $d+8$. Explicit examples of these objects are constructed for every integer value of the degree, $d\ge 6$, $d\ne 7$. Furthermore, it is shown that when $d=6$ this space is isomorphic to the group $G_2({\mathbb C})$, and when $d=7$ this space is empty. We also show that the dimension of the space of nonlinearly full almost complex 2-spheres of area $4\pi d$ in the round 6-sphere is $2d+5$.

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