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Symplectic hypersurfaces in 
Author:
R. Hind
Journal:
Proc. Amer. Math. Soc. 134 (2006), 1205-1211
MSC (2000):
Primary 57R17; Secondary 57R95
Posted:
July 20, 2005
MathSciNet review:
2196058
Full-text PDF Free Access
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Abstract: We establish the uniqueness of the symplectic  -manifolds which admit low degree symplectic embeddings into  . We also discuss the uniqueness of the fundamental group of the complement of such embeddings into arbitrary symplectic  -manifolds.
- 1.
D.
Auroux, Asymptotically holomorphic families of symplectic
submanifolds, Geom. Funct. Anal. 7 (1997),
no. 6, 971–995. MR 1487750
(99b:57069), http://dx.doi.org/10.1007/s000390050033
- 2.
S.
K. Donaldson, Symplectic submanifolds and almost-complex
geometry, J. Differential Geom. 44 (1996),
no. 4, 666–705. MR 1438190
(98h:53045)
- 3.
M.
Gromov, Pseudoholomorphic curves in symplectic manifolds,
Invent. Math. 82 (1985), no. 2, 307–347. MR 809718
(87j:53053), http://dx.doi.org/10.1007/BF01388806
- 4.
Mikhael
Gromov, Partial differential relations, Ergebnisse der
Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related
Areas (3)], vol. 9, Springer-Verlag, Berlin, 1986. MR 864505
(90a:58201)
- 5.
Dusa
McDuff, The structure of rational and ruled
symplectic 4-manifolds, J. Amer. Math. Soc.
3 (1990), no. 3,
679–712. MR 1049697
(91k:58042), http://dx.doi.org/10.1090/S0894-0347-1990-1049697-8
- 6.
Dusa
McDuff, The local behaviour of holomorphic curves in almost complex
4-manifolds, J. Differential Geom. 34 (1991),
no. 1, 143–164. MR 1114456
(93e:53050)
- 7.
Dusa
McDuff, Symplectic manifolds with contact type boundaries,
Invent. Math. 103 (1991), no. 3, 651–671. MR 1091622
(92e:53042), http://dx.doi.org/10.1007/BF01239530
- 8.
Dusa
McDuff and Dietmar
Salamon, 𝐽-holomorphic curves and quantum cohomology,
University Lecture Series, vol. 6, American Mathematical Society,
Providence, RI, 1994. MR 1286255
(95g:58026)
- 9.
Dusa
McDuff and Dietmar
Salamon, 𝐽-holomorphic curves and symplectic topology,
American Mathematical Society Colloquium Publications, vol. 52,
American Mathematical Society, Providence, RI, 2004. MR 2045629
(2004m:53154)
- 10.
B. Siebert and G. Tian, On the holomorphicity of genus two Lefschetz fibrations, preprint math.SG/0305343.
- 1.
- D. Auroux, Asymptotically holomorphic families of symplectic submanifolds, Geom. Funct. Anal., 7(1997), no. 6, 971-995. MR 1487750 (99b:57069)
- 2.
- S. K. Donaldson, Symplectic submanifolds and almost-complex geometry, J. Differential Geom., 44(1996), no. 4, 666-705. MR 1438190 (98h:53045)
- 3.
- M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, Inv. Math., 82(1985), 307-347. MR 0809718 (87j:53053)
- 4.
- M. Gromov, Partial differential relations, Springer-Verlag, Berlin, 1986. MR 0864505 (90a:58201)
- 5.
- D. McDuff, The structure of rational and ruled symplectic
 -manifolds, J. Amer. Math. Soc., 3(1990), no. 3, 679-712. MR 1049697 (91k:58042)
- 6.
- D. McDuff, The local behaviour of
 -holomorphic curves in almost complex  -manifolds, J. Diff. Geom., 34(1991), 143-164. MR 1114456 (93e:53050)
- 7.
- D. McDuff, Symplectic manifolds with contact type boundaries, Inv. Math., 103(1991), no. 3, 651-671. MR 1091622 (92e:53042)
- 8.
- D. McDuff and D. Salamon,
 -holomorphic curves and quantum cohomology. University Lecture Series, 6, American Mathematical Society, Providence, RI, 1994. MR 1286255 (95g:58026)
- 9.
- D. McDuff and D. Salamon,
 -holomorphic curves and symplectic topology. American Mathematical Society Colloquium Publications, 52, American Mathematical Society, Providence, RI, 2004. MR 2045629 (2004m:53154)
- 10.
- B. Siebert and G. Tian, On the holomorphicity of genus two Lefschetz fibrations, preprint math.SG/0305343.
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Additional Information
R. Hind
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46601
Email:
hind.1@nd.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08054-8
PII:
S 0002-9939(05)08054-8
Received by editor(s):
September 24, 2004
Received by editor(s) in revised form:
October 22, 2004
Posted:
July 20, 2005
Additional Notes:
This work was supported in part by NSF grant DMS-0204634.
Communicated by:
Jon G. Wolfson
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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