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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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 $2d+5$.
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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