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- W2953663344 abstract "Taubes has recently defined Gromov invariants for symplectic four-manifolds and related them to the Seiberg-Witten invariants. Independently, Ruan and Tian defined symplectic invariants based on ideas of Witten. In this note, we show that Taubes' Gromov invariants are equal to certain combinations of Ruan-Tian invariants. This link allows us to generalize Taubes' invariants. For each closed symplectic four-manifold, we define a sequence of symplectic invariants $Gr_{delta}$, $delta=0,1,2,...$. The first of these, $Gr_0$, generates Taubes' invariants, which count embedded J-holomorphic curves. The new invariants $Gr_{delta}$ count immersed curves with $delta$ double points. In particular, these results give an independent proof that Taubes' invariants are well-defined. They also show that some of the Ruan-Tian symplectic invariants agree with the Seiberg-Witten invariants." @default.
- W2953663344 created "2019-07-12" @default.
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- W2953663344 date "1997-02-06" @default.
- W2953663344 modified "2023-09-27" @default.
- W2953663344 title "The Gromov Invariants of Ruan-Tian and Taubes" @default.
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