An index inequality for embedded pseudoholomorphic curves in symplectizations

Hutchings, Michael. "An index inequality for embedded pseudoholomorphic curves in symplectizations." Journal of the European Mathematical Society 004.4 (2002): 313-361. <http://eudml.org/doc/277717>.

@article{Hutchings2002,
abstract = {Let $\Sigma $ be a surface with a symplectic form, let $\phi $ be a symplectomorphism of $\Sigma $, and let $Y$ be the mapping torus of $\phi $. We show that the dimensions of moduli spaces of embedded pseudoholomorphic curves in $\mathbb \{R\}\times \mathbb \{Y\}$, with cylindrical ends asymptotic to periodic orbits of $\phi $ or multiple covers thereof, are bounded from above by an additive relative index. We deduce some compactness results for these moduli spaces. This paper establishes some of the foundations for a program with Michael Thaddeus, to understand the Seiberg-Witten Floer homology of $Y$ in terms of such pseudoholomorphic curves. Analogues of our results should also hold in three dimensional contact topology.},
author = {Hutchings, Michael},
journal = {Journal of the European Mathematical Society},
keywords = {pseudoholomorphic curves; period orbits; mapping torus; pseudoholomorphic curves; period orbits; mapping torus},
language = {eng},
number = {4},
pages = {313-361},
publisher = {European Mathematical Society Publishing House},
title = {An index inequality for embedded pseudoholomorphic curves in symplectizations},
url = {http://eudml.org/doc/277717},
volume = {004},
year = {2002},
}

TY - JOUR
AU - Hutchings, Michael
TI - An index inequality for embedded pseudoholomorphic curves in symplectizations
JO - Journal of the European Mathematical Society
PY - 2002
PB - European Mathematical Society Publishing House
VL - 004
IS - 4
SP - 313
EP - 361
AB - Let $\Sigma $ be a surface with a symplectic form, let $\phi $ be a symplectomorphism of $\Sigma $, and let $Y$ be the mapping torus of $\phi $. We show that the dimensions of moduli spaces of embedded pseudoholomorphic curves in $\mathbb {R}\times \mathbb {Y}$, with cylindrical ends asymptotic to periodic orbits of $\phi $ or multiple covers thereof, are bounded from above by an additive relative index. We deduce some compactness results for these moduli spaces. This paper establishes some of the foundations for a program with Michael Thaddeus, to understand the Seiberg-Witten Floer homology of $Y$ in terms of such pseudoholomorphic curves. Analogues of our results should also hold in three dimensional contact topology.
LA - eng
KW - pseudoholomorphic curves; period orbits; mapping torus; pseudoholomorphic curves; period orbits; mapping torus
UR - http://eudml.org/doc/277717
ER -