On $J$-holomorphic curves in almost complex manifolds with asymptotically cylindrical ends

Erkao Bao

Vol. 278 (2015), No. 2, 291–324

DOI: 10.2140/pjm.2015.278.291

Abstract

Symplectic field theory is the study of $J$-holomorphic curves in almost complex manifolds with cylindrical ends. One natural generalization is to replace “cylindrical” by “asymptotically cylindrical”. We generalize a number of asymptotic results about the behavior of $J$-holomorphic curves near infinity to the asymptotically cylindrical setting. We also sketch how these asymptotic results allow compactness theorems in symplectic field theory to be extended to the asymptotically cylindrical case.

Keywords

asymptotically cylindrical almost complex structure, symplectic field theory, compactness, Hofer energy, $J$-holomorphic curve, Morse–Bott, stable Hamiltonian structure

Mathematical Subject Classification 2010

Primary: 53D05, 53D10, 53D12, 53D40, 53D42

Secondary: 58J05

Milestones

Received: 19 January 2014

Revised: 21 April 2015

Accepted: 22 April 2015

Published: 6 October 2015