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2011 Knotted Legendrian surfaces with few Reeb chords
Georgios Dimitroglou Rizell
Algebr. Geom. Topol. 11(5): 2903-2936 (2011). DOI: 10.2140/agt.2011.11.2903

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.

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Georgios Dimitroglou Rizell. "Knotted Legendrian surfaces with few Reeb chords." Algebr. Geom. Topol. 11 (5) 2903 - 2936, 2011. https://doi.org/10.2140/agt.2011.11.2903

Information

Received: 4 February 2011; Revised: 23 June 2011; Accepted: 4 August 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1248.53073
MathSciNet: MR2846915
Digital Object Identifier: 10.2140/agt.2011.11.2903

Subjects:
Primary: 53D42
Secondary: 53D12

Rights: Copyright © 2011 Mathematical Sciences Publishers

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