Algebraic & Geometric Topology 11 (2011) 2903–2936

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(R²) = R⁵ 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 Z₂, 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

Primary: 53D42

Secondary: 53D12

References

Publication

Received: 4 February 2011
Revised: 23 June 2011
Accepted: 4 August 2011
Published: 23 October 2011

Authors