Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Symplectic hypersurfaces in $\mathbb{C} P^3$

Author(s): R. Hind
Journal: Proc. Amer. Math. Soc. 134 (2006), 1205-1211.
MSC (2000): Primary 57R17; Secondary 57R95
Posted: July 20, 2005
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We establish the uniqueness of the symplectic $4$-manifolds which admit low degree symplectic embeddings into ${\mathbb C} P^3$. We also discuss the uniqueness of the fundamental group of the complement of such embeddings into arbitrary symplectic $6$-manifolds.

References:

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 $4$-manifolds, J. Amer. Math. Soc., 3(1990), no. 3, 679-712. MR 1049697 (91k:58042)

6.
D. McDuff, The local behaviour of $J$-holomorphic curves in almost complex $4$-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, $J$-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, $J$-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.

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 57R17, 57R95

Retrieve articles in all Journals with MSC (2000): 57R17, 57R95

Additional Information:

R. Hind
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46601
Email: hind.1@nd.edu

DOI: 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
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google