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

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- by Luis Fernández PDF
- 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 $2d+5$.## References

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## Additional Information

**Luis Fernández**- Affiliation: Department of Mathematics and Computer Science, Bronx Community College of CUNY, 2155 University Avenue, Bronx, New York 10453
- Email: luis.fernandez01@bcc.cuny.edu, lmfernand@gmail.com
- Received by editor(s): July 29, 2012
- Published electronically: November 24, 2014
- Additional Notes: The author was partially supported by a PSC-CUNY grant.
- © Copyright 2014
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**367**(2015), 2437-2458 - MSC (2010): Primary 58D10, 58E20; Secondary 32Q60
- DOI: https://doi.org/10.1090/S0002-9947-2014-06070-4
- MathSciNet review: 3301869