Volume 11, issue 5 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Knotted Legendrian surfaces with few Reeb chords

Georgios Dimitroglou Rizell

Algebraic & Geometric Topology 11 (2011) 2903–2936
Abstract

For g > 0, we construct g + 1 Legendrian embeddings of a surface of genus g into J1(2) = 5 which lie in pairwise distinct Legendrian isotopy classes and which all have g + 1 transverse Reeb chords (g + 1 is the conjecturally minimal number of chords). Furthermore, for g of the g + 1 embeddings the Legendrian contact homology DGA does not admit any augmentation over 2, and hence cannot be linearized. We also investigate these surfaces from the point of view of the theory of generating families. Finally, we consider Legendrian spheres and planes in J1(S2) from a similar perspective.

Keywords
Legendrian surface, Legendrian contact homology, gradient flow tree, generating function
Mathematical Subject Classification 2010
Primary: 53D42
Secondary: 53D12
References
Publication
Received: 4 February 2011
Revised: 23 June 2011
Accepted: 4 August 2011
Published: 23 October 2011
Authors
Georgios Dimitroglou Rizell
Department of mathematics
Uppsala University
Box 480
751 06 Uppsala
Sweden