Knotted Legendrian surfaces with few Reeb chords

Dimitroglou Rizell, Georgios¹

¹Department of mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden

Algebraic and Geometric Topology, Tome 11 (2011) no. 5, pp. 2903-2936

Résumé

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.

Détail

DOI : 10.2140/agt.2011.11.2903

Classification : 53D42, 53D12
Keywords: Legendrian surface, Legendrian contact homology, gradient flow tree, generating function

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