Branch Structure Of J-Holomorphic Curves Near Periodic Orbits Of A Contact Manifold

Title
Branch Structure Of J-Holomorphic Curves Near Periodic Orbits Of A Contact Manifold
Publication Date
2008
Author(s)
Harris, Adam
( author )
OrcID: https://orcid.org/0000-0002-1259-1122
Email: aharris5@une.edu.au
UNE Id une-id:aharris5
Wysocki, Krzysztof
Type of document
Journal Article
Language
en
Entity Type
Publication
Publisher
American Mathematical Society
Place of publication
United States of America
UNE publication id
une:3401
Abstract
Let M be a three–dimensional contact manifold, and ψ : D \{0} → M x ℝ a finite–energy pseudoholomorphic map from the punctured disc in ℂ that is asymptotic to a periodic orbit of the contact form. This article examines conditions under which smooth coordinates may be defined in a tubular neighbourhood of the orbit such that ψ resembles a holomorphic curve, invoking comparison with the theory of topological linking of plane complex algebroid curves near a singular point. Examples of this behaviour, which are studied in some detail, include pseudoholomorphic maps into Ep,q x R, where Ep,q denotes a rational ellipsoid (contact structure induced by the standard complex structure on ℂ²), as well as contact structures arising from non-standard circle–fibrations of the three–sphere.
Link
Citation
Transactions of the American Mathematical Society, 360(4), p. 2131-2152
ISSN
1088-6850
0002-9947
Start page
2131
End page
2152

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