# An index inequality for embedded pseudoholomorphic curves in symplectizations

Journal of the European Mathematical Society (2002)

- Volume: 004, Issue: 4, page 313-361
- ISSN: 1435-9855

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topHutchings, 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 -

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