Symplectic geometry on moduli spaces of J-holomorphic curves

Details Symplectic geometry on moduli spaces of J-holomorphic curves Symplectic geometry on moduli spaces of J-holomorphic curves

2009-05-19

arxiv.org/abs/0905.3009v2

Mathematics

Symplectic Geometry

16 pages

Scientific paper

10.1007/s10455-011-9281-1

Let (M,\omega) be a symplectic manifold, and Sigma a compact Riemann surface. We define a 2-form on the space of immersed symplectic surfaces in M, and show that the form is closed and non-degenerate, up to reparametrizations. Then we give conditions on a compatible almost complex structure J on (M,\omega) that ensure that the restriction of the form to the moduli space of simple immersed J-holomorphic Sigma-curves in a homology class A in H_2(M,\Z) is a symplectic form, and show applications and examples. In particular, we deduce sufficient conditions for the existence of J-holomorphic Sigma-curves in a given homology class for a generic J.

Affiliated with

Also associated with

No associations

Rating

Symplectic geometry on moduli spaces 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 Symplectic geometry on moduli spaces of J-holomorphic curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Symplectic geometry on moduli spaces of J-holomorphic curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-699211