Lectures on Gromov invariants for symplectic 4-manifolds

Details Lectures on Gromov invariants for symplectic 4-manifolds Lectures on Gromov invariants for symplectic 4-manifolds

1996-06-18

arxiv.org/abs/dg-ga/9606005v1

Mathematics

Differential Geometry

Latex, 42 pages

Scientific paper

These are notes of lectures given at the NATO Summer School, Montreal 1995. Taubes's recent spectacular work setting up a correspondence between $J$-holomorphic curves in symplectic 4-manifolds and solutions of the Seiberg-Witten equations counts $J$-holomorphic curves in a somewhat new way. The "standard" theory concerns itself with moduli spaces of connected curves, and gives rise to Gromov-Witten invariants. However, Taubes's curves arise as zero sets of sections and so need not be connected. These notes are in the main expository. We first discuss the invariants as Taubes defined them, and then discuss some alternatives, showing, for example, a way of dealing with multiply-covered exceptional spheres. We also calculate some examples, in particular finding the Gromov invariant of the fiber class of an elliptic surface by counting $J$-holomorphic curves, rather than going via Seiberg--Witten theory.

Affiliated with

Also associated with

No associations

Rating

Lectures on Gromov invariants for symplectic 4-manifolds 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 Lectures on Gromov invariants for symplectic 4-manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lectures on Gromov invariants for symplectic 4-manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-586535