Algebraic & Geometric Topology

Knotted Legendrian surfaces with few Reeb chords

Georgios Dimitroglou Rizell

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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.

Article information

Algebr. Geom. Topol., Volume 11, Number 5 (2011), 2903-2936.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D42: Symplectic field theory; contact homology
Secondary: 53D12: Lagrangian submanifolds; Maslov index

Legendrian surface Legendrian contact homology gradient flow tree generating function


Dimitroglou Rizell, Georgios. Knotted Legendrian surfaces with few Reeb chords. Algebr. Geom. Topol. 11 (2011), no. 5, 2903--2936. doi:10.2140/agt.2011.11.2903.

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