The Gromov Invariants of Ruan-Tian and Taubes
Autor: | Thomas H. Parker, Eleny-Nicoleta Ionel |
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Jazyk: | angličtina |
Rok vydání: | 1997 |
Předmět: |
Sequence
Pure mathematics Stable curve General Mathematics Mathematical analysis Mathematics::Geometric Topology Tian High Energy Physics::Theory Mathematics - Algebraic Geometry Gromov–Witten invariant FOS: Mathematics Mathematics::Differential Geometry Link (knot theory) Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Mathematics Symplectic geometry |
Popis: | 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. Comment: AMS-LaTeX, 11 pages |
Databáze: | OpenAIRE |
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