Branch structure of -holomorphic curves near periodic orbits of a contact manifold

Authors:
Adam Harris and Krzysztof Wysocki

Journal:
Trans. Amer. Math. Soc. **360** (2008), 2131-2152

MSC (2000):
Primary 32Q65, 53D10

Published electronically:
October 30, 2007

MathSciNet review:
2366977

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a three-dimensional contact manifold, and a finite-energy pseudoholomorphic map from the punctured disc in 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 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 , where denotes a rational ellipsoid (contact structure induced by the standard complex structure on ), as well as contact structures arising from non-standard circle-fibrations of the three-sphere.

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Additional Information

**Adam Harris**

Affiliation:
School of Mathematics, Statistics and Computer Science, University of New England, Armidale, NSW 2351, Australia

Email:
adamh@turing.une.edu.au

**Krzysztof Wysocki**

Affiliation:
School of Mathematics and Statistics, Melbourne University, Parkville, VIC 3010, Australia

Email:
wysocki@ms.unimelb.edu.au

DOI:
https://doi.org/10.1090/S0002-9947-07-04350-4

Received by editor(s):
July 18, 2005

Received by editor(s) in revised form:
June 1, 2006

Published electronically:
October 30, 2007

Article copyright:
© Copyright 2007
American Mathematical Society