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


Author: Luis Fernández
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
Published electronically: November 24, 2014
MathSciNet review: 3301869
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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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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

DOI: https://doi.org/10.1090/S0002-9947-2014-06070-4
Received by editor(s): July 29, 2012
Published electronically: November 24, 2014
Additional Notes: The author was partially supported by a PSC-CUNY grant.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.