Higher jet evaluation transversality of $J$-holomorphic curves

Details Higher jet evaluation transversality of $J$-holomorphic curves Higher jet evaluation transversality of $J$-holomorphic curves

2009-04-22

arxiv.org/abs/0904.3573v2

J. Korean Math. Soc. 48 (2011), 341-365

Mathematics

Symplectic Geometry

22 pages, no figure; v2 minor typos corrected

Scientific paper

In this paper, we establish general stratawise higher jet evaluation transversality of $J$-holomorphic curves for a generic choice of almost complex structures $J$ tame to a given symplectic manifold $(M,\omega)$. Using this transversality result, we prove that there exists a subset $\CJ_\omega^{ram} \subset \CJ_\omega$ of second category such that for every $J \in \CJ_\omega^{ram}$, the dimension of the moduli space of (somewhere injective) $J$-holomorphic curves with a given ramification profile goes down by $2n$ or $2(n-1)$ depending on whether the ramification degree goes up by one or a new ramification point is created. We also derive that for each $J \in \CJ_\omega^{ram}$ there are only a finite number of ramification profiles of $J$-holomorphic curves in a given homology class $\beta \in H_2(M;\Z)$ and provide an explicit upper bound on the number of ramification profiles in terms of $c_1(\beta)$ and the genus $g$ of the domain surface.

Affiliated with

Also associated with

No associations

Rating

Higher jet evaluation transversality of $J$-holomorphic curves 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 Higher jet evaluation transversality of $J$-holomorphic curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Higher jet evaluation transversality of $J$-holomorphic curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-408288