Knotted Legendrian surfaces with few Reeb chords

Details Knotted Legendrian surfaces with few Reeb chords Knotted Legendrian surfaces with few Reeb chords

2011-02-04

arxiv.org/abs/1102.0914v2

Mathematics

Symplectic Geometry

30 pages, 11 figures

Scientific paper

10.2140/agt.2011.11.2903

For $g>0$, we construct $g+1$ Legendrian embeddings of a surface of genus $g$ into $J^1(R^2)=R^5$ 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 $Z/2Z$, 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 $J^1(S^2)$ from a similar perspective.

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