Relative ruan and gromov-taubes invariants of symplectic 4-manifolds

Josef G. Dorfmeister, Tian Jun Li

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Abstract

We define relative Ruan invariants that count embedded connected symplectic submanifolds which contact a fixed symplectic hypersurface V in a symplectic 4-manifold (X, ω) at prescribed points with prescribed contact orders (in addition to insertions on X\V). We obtain invariants of the deformation class of (X, V, ω). Two large issues must be tackled to define such invariants: (1) curves lying in the hypersurface V and (2) genericity results for almost complex structures constrained to make V pseudo-holomorphic (or almost complex). Moreover, these invariants are refined to take into account rim-tori decompositions. In the latter part of the paper, we extend the definition to disconnected submanifolds and construct relative Gromov-Taubes invariants.

Original languageEnglish (US)
Article number1250062
JournalCommunications in Contemporary Mathematics
Volume15
Issue number1
DOIs
StatePublished - Feb 2013

Keywords

  • Relative Gromov-Taubes invariants
  • Relative Ruan invariants
  • Symplectic 4-manifolds

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