Mathematics – Symplectic Geometry
Scientific paper
1999-12-18
Mathematics
Symplectic Geometry
Ph.D. Thesis (U.A.M., Spain; April 1999), 159 pages
Scientific paper
Our aim in this work is to study a system of equations which generalises at the same time the vortex equations of Yang-Mills-Higgs theory and the holomorphicity equation in Gromov theory of pseudoholomorphic curves. We extend some results and definitions from both theories to a common setting. We introduce a functional generalising Yang-Mills-Higgs functional, whose minima coincide with the solutions to our equations. We prove a Hitchin-Kobayashi correspondence allowing to study the solutions of the equations in the Kaehler case. We give a structure of smooth manifold to the set of (gauge equivalence classes of) solutions to (a perturbation of) the equations (the so-called moduli space). We give a compactification of the moduli space, generalising Gromov's compactification of the moduli of holomorphic curves. Finally, we use the moduli space to define (under certain conditions) invariants of compact symplectic manifolds with a Hamiltonian almost free action of S^1. These invariants generalise Gromov-Witten invariants. This is the author's Ph.D. Thesis. A chapter of it is contained in the paper math.DG/9901076. After submitting his thesis in April 1999, the author knew that K. Cieliebak, A. R. Gaio and D. Salamon had also arrived (from a different point of view) at the same equations, and had developed a very similar programme (see math.SG/9909122).
No associations
LandOfFree
Yang-Mills-Higgs theory for symplectic fibrations 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 Yang-Mills-Higgs theory for symplectic fibrations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Yang-Mills-Higgs theory for symplectic fibrations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-600568