Compactness for embedded pseudoholomorphic curves in 3-manifolds

Wendl, Chris. "Compactness for embedded pseudoholomorphic curves in 3-manifolds." Journal of the European Mathematical Society 012.2 (2010): 313-342. <http://eudml.org/doc/277597>.

@article{Wendl2010,
abstract = {We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem [BEH+C03] by using intersection theory to show that degenerations of such sequences never give rise to multiple covers or nodes, so transversality is easily achieved. This has application to the theory of stable finite energy foliations introduced in [HWZ03], and also suggests a new approach to defining SFT-type invariants for contact 3-manifolds, or more generally, 3-manifolds with stable Hamiltonian structures.},
author = {Wendl, Chris},
journal = {Journal of the European Mathematical Society},
keywords = {pseudoholomorphic curves; finite energy surfaces; stable Hamiltonian; pseudoholomorphic curves; finite energy surfaces; stable Hamiltonian structures},
language = {eng},
number = {2},
pages = {313-342},
publisher = {European Mathematical Society Publishing House},
title = {Compactness for embedded pseudoholomorphic curves in 3-manifolds},
url = {http://eudml.org/doc/277597},
volume = {012},
year = {2010},
}

TY - JOUR
AU - Wendl, Chris
TI - Compactness for embedded pseudoholomorphic curves in 3-manifolds
JO - Journal of the European Mathematical Society
PY - 2010
PB - European Mathematical Society Publishing House
VL - 012
IS - 2
SP - 313
EP - 342
AB - We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem [BEH+C03] by using intersection theory to show that degenerations of such sequences never give rise to multiple covers or nodes, so transversality is easily achieved. This has application to the theory of stable finite energy foliations introduced in [HWZ03], and also suggests a new approach to defining SFT-type invariants for contact 3-manifolds, or more generally, 3-manifolds with stable Hamiltonian structures.
LA - eng
KW - pseudoholomorphic curves; finite energy surfaces; stable Hamiltonian; pseudoholomorphic curves; finite energy surfaces; stable Hamiltonian structures
UR - http://eudml.org/doc/277597
ER -