Abstract
The chapter is devoted to the study of the intersection theory of holomorphic curves in (real) four-dimensional almost complex manifolds. Some of the ideas originate from McDuff’s work in [84], see also [85], which in turn was influenced by Gromov’s seminal paper [60]. Other important work in this direction is [89] and [104].
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References
C. Abbas, Finite energy surfaces and the chord problem. Duke Math. J. 96, 241–316 (1999)
M. Gromov, Pseuodoholomorphic curves in symplectic manifolds. Invent. Math. 82, 307–347 (1985)
D. McDuff, Singularities of J-holomorphic curves in almost complex 4-manifolds. J. Geom. Anal. 2(3), 249–266 (1992)
D. McDuff, Singularities and positivity of intersections of J-holomorphic curves, in Holomorphic Curves in Symplectic Geometry. Volume 117 of Progress in Mathematics (Birkha̋user, Basel, 1994), pp. 191–215. With an appendix by Gang Liu
M. Micallef, B. White, The structure of branch points in minimal surfaces and in pseudoholomorphic curves. Ann. Math. (2) 141(1), 35–85 (1995)
R. Siefring, Relative asymptotic behavior of pseudoholomorphic half-cylinders. Commun. Pure Appl. Math. 61(12), 1631–1684 (2008)
R. Siefring, Intersection theory of punctured pseudoholomorphic curves. Geom. Topol. 15(4), 2351–2457 (2011)
J.-C. Sikorav, Singularities of J-holomorphic curves. Math. Z. 226(3), 359–373 (1997)
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Abbas, C., Hofer, H. (2019). Intersection Theory for Pseudoholomorphic Disks. In: Holomorphic Curves and Global Questions in Contact Geometry. Birkhäuser Advanced Texts Basler Lehrbücher. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-11803-7_6
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DOI: https://doi.org/10.1007/978-3-030-11803-7_6
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