Compactness results in Symplectic Field Theory

This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in (4). We prove compactness results for moduli spaces of holomorphic curves arising in Symplectic Field Theory. The theorems generalize Gromov's compactness theorem in (8) as well as compactness theorems in Floer homology theory, (6, 7), and in contact geometry, (9, 19).

[1]  E. Zehnder,et al.  Finite energy foliations of tight three-spheres and Hamiltonian dynamics , 2003 .

[2]  John B. Etnyre,et al.  Legendrian Submanifolds in $R^{2n+1}$ and Contact Homology , 2002, math/0210124.

[3]  E. Zehnder,et al.  Finite energy cylinders of small area , 2002, Ergodic Theory and Dynamical Systems.

[4]  F. Bourgeois.  A Morse-Bott approach to contact homology , 2002 .

[5]  Jun Li.  A Degeneration Formula of GW-Invariants , 2001, math/0110113.

[6]  E. Zehnder,et al.  The asymptotic behavior of a finite energy plane , 2001 .

[7]  Thomas H. Parker,et al.  The symplectic sum formula for Gromov–Witten invariants , 2000, 1510.06943.

[8]  H. Hofer,et al.  Introduction to Symplectic Field Theory , 2000, math/0010059.

[9]  Thomas H. Parker,et al.  Relative Gromov-Witten invariants , 1999, math/9907155.

[10]  E. Zehnder,et al.  Properties of Pseudoholomorphic Curves in Symplectizations III: Fredholm Theory , 1999 .

[11]  E. Zehnder,et al.  The dynamics on three-dimensional strictly convex energy surfaces , 1998 .

[12]  E. Zehnder,et al.  Correction to “Properties of pseudoholomorphic curves in symplectisations I: Asymptotics” , 1998 .

[13]  An-Min Li,et al.  Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds , 1998, math/9803036.

[14]  C. Thomas.  Contact and symplectic geometry , 1996 .

[15]  E. Zehnder,et al.  Properties of pseudoholomorphic curves in symplectisations. I : asymptotics , 1996 .

[16]  E. Zehnder,et al.  Properties of Pseudoholomorphic Curves in Symplectisations Iv: Asymptotics with Degeneracies , 1996 .

[17]  D. Salamon,et al.  Lagrangian intersections in Contact geometry , 1995 .

[18]  Eduard Zehnder,et al.  Symplectic Invariants and Hamiltonian Dynamics , 1994 .

[19]  R. Ye.  Gromov’s compactness theorem for pseudo holomorphic curves , 1994 .

[20]  D. Salamon,et al.  J-Holomorphic Curves and Quantum Cohomology , 1994 .

[21]  Marie-Paule Muller.  Gromov’s Schwarz lemma as an estimate of the gradient for holomorphic curves , 1994 .

[22]  H. Hofer.  Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three , 1993 .

[23]  H. Hofer,et al.  The weinstein conjecture in the presence of holomorphic spheres , 1992 .

[24]  Claude Viterbo,et al.  An introduction to symplectic topology , 1991 .

[25]  A. Floer,et al.  The unregularized gradient flow of the symplectic action , 1988 .

[26]  A. Floer,et al.  Morse theory for Lagrangian intersections , 1988 .

[27]  S. Wolpert.  ON THE WEIL-PETERSSON GEOMETRY OF THE MODULI SPACE OF CURVES , 1985 .

[28]  M. Gromov.  Pseudo holomorphic curves in symplectic manifolds , 1985 .

[29]  D. Mumford,et al.  The irreducibility of the space of curves of given genus , 1969 .