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Almost complex rigidity of the complex projective plane
Author(s):
Benjamin
McKay
Journal:
Proc. Amer. Math. Soc.
135
(2007),
597-603.
MSC (2000):
Primary 57R17, 51A10;
Secondary 14N05
Posted:
August 8, 2006
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Abstract:
An isomorphism of symplectically tame smooth pseudocomplex structures on the complex projective plane which is a homeomorphism and differentiable of full rank at two points is smooth.
References:
-
- 1.
- B. Coupet, H. Gaussier, and A. Sukhov, Riemann maps in almost complex manifolds, arXiv:math.CV/0307332, July 2003.
- 2.
- J. J. Duistermaat, On first order elliptic equations for sections of complex line bundles, Compositio Math. 25 (1972), 237-243. MR 0367476 (51:3718)
- 3.
- Mikhael Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), no. 2, 307-347. MR 0809718 (87j:53053)
- 4.
- Benjamin McKay, Duality and integrable systems of pseudoholomorphic curves, Ph.D. thesis, Duke University, Durham, N.C., 1999.
- 5.
- -, Dual curves and pseudoholomorphic curves, Selecta Math. (N.S.) 9 (2003), no. 2, 251-311. MR 1993485 (2004g:53099)
- 6.
- Helmut Salzmann, Dieter Betten, Theo Grundhöfer, Hermann Hähl, Rainer Löwen, and Markus Stroppel, Compact projective planes, de Gruyter Expositions in Mathematics, vol. 21, Walter de Gruyter & Co., Berlin, 1995, with an introduction to octonion geometry. MR 1384300 (97b:51009)
- 7.
- Clifford Henry Taubes, The Seiberg-Witten and Gromov invariants, Math. Res. Lett. 2 (1995), no. 2, 221-238. MR 1324704 (96a:57076)
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Additional Information:
Benjamin
McKay
Affiliation:
School of Mathematical Sciences, University College Cork, Cork, Ireland
Email:
B.McKay@UCC.ie
DOI:
10.1090/S0002-9939-06-08492-9
PII:
S 0002-9939(06)08492-9
Received by editor(s):
April 2, 2004
Received by editor(s) in revised form:
September 2, 2005
Posted:
August 8, 2006
Additional Notes:
This work was supported in full or in part by a grant from the University of South Florida St. Petersburg New Investigator Research Grant Fund. This support does not necessarily imply endorsement by the University of research conclusions.
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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