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Proceedings of the American Mathematical Society

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Embedded surfaces
and almost complex structures


Author: Christian Bohr
Journal: Proc. Amer. Math. Soc. 128 (2000), 2147-2154
MSC (1991): Primary 53C15, 57R95
DOI: https://doi.org/10.1090/S0002-9939-99-05277-6
Published electronically: October 29, 1999
MathSciNet review: 1657766
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we prove necessary and sufficient conditions for a smooth surface in a smooth 4-manifold $X$ to be pseudoholomorphic with respect to an almost complex structure on $X$. In particular, this provides a systematic approach to the construction of pseudoholomorphic curves that do not minimize the genus in their homology class.


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  • [D] S.K. Donaldson, Connections, cohomology and the intersection form of 4-manifolds, J. Differential Geom. 24 (1986), 275-342. MR 88g:57033
  • [HH] F. Hirzebruch, H. Hopf, Felder von Flächenelementen in 4-dimensionalen Mannigfaltigkeiten, Math. Ann. 136, (1958) 156-172. MR 20:7272
  • [Fu] M. Furuta, Monopole equation and the 11/8-conjecture, Preprint, 1995.
  • [MH] J. Milnor, D. Husemoller, Symmetric bilinear forms, Springer-Verlag, 1973. MR 58:22129
  • [Mi] G. Mikhalkin, J-holomorphic curves do not always minimize the genus, Proc. Amer. Math. Soc, 125 (1997), 1831-1833. MR 97g:57047
  • [W1] C.T.C. Wall, On the orthogonal groups of unimodular quadratic forms, Math. Ann. 147 (1962), 328-338. MR 25:2009
  • [W2] C.T.C. Wall, Diffeomorphisms of 4-manifolds, J. London Math. Soc. 39 (1964), 131-140. MR 29:626
  • [W] H. Whitney, On the topology of differentiable manifolds, Lectures in Topology, Ann Arbor, Michigan, 1941. MR 3:133a

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Additional Information

Christian Bohr
Affiliation: Mathematisches Institut der LMU, Theresienstr. 39, 80333 München, Germany
Email: bohr@rz.mathematik.uni-muenchen.de

DOI: https://doi.org/10.1090/S0002-9939-99-05277-6
Received by editor(s): August 17, 1998
Published electronically: October 29, 1999
Additional Notes: This work has been supported by the Graduiertenkolleg “Mathematik im Bereich ihrer Wechselwirkung mit der Physik”
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2000 American Mathematical Society

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