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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Filling by holomorphic curves in
symplectic 4-manifolds


Author: Rugang Ye
Journal: Trans. Amer. Math. Soc. 350 (1998), 213-250
MSC (1991): Primary 53C15; Secondary 32C25
MathSciNet review: 1422913
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Abstract: We develop a general framework for embedded (immersed) $J$-holomorphic curves and a systematic treatment of the theory of filling by holomorphic curves in 4-dimensional symplectic manifolds. In particular, a deformation theory and an intersection theory for $J$-holomorphic curves with boundary are developed. Bishop's local filling theorem is extended to almost complex manifolds. Existence and uniqueness of global fillings are given complete proofs. Then they are extended to the situation with nontrivial $J$-holomorphic spheres, culminating in the construction of singular fillings.


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Additional Information

Rugang Ye
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: yer@math.ucsb.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-01970-9
PII: S 0002-9947(98)01970-9
Received by editor(s): January 24, 1996
Additional Notes: Partially supported by NSF
Article copyright: © Copyright 1998 American Mathematical Society