The Gromov Invariants of Ruan-Tian and Taubes

Details The Gromov Invariants of Ruan-Tian and Taubes The Gromov Invariants of Ruan-Tian and Taubes

1997-02-06

arxiv.org/abs/alg-geom/9702008v1

Mathematics

Algebraic Geometry

AMS-LaTeX, 11 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The Gromov Invariants of Ruan-Tian and Taubes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Gromov Invariants of Ruan-Tian and Taubes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Gromov Invariants of Ruan-Tian and Taubes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-73569