Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 11, Number 5 (2011), 2903-2936.
Knotted Legendrian surfaces with few Reeb chords
For , we construct Legendrian embeddings of a surface of genus into which lie in pairwise distinct Legendrian isotopy classes and which all have transverse Reeb chords ( is the conjecturally minimal number of chords). Furthermore, for of the embeddings the Legendrian contact homology DGA does not admit any augmentation over , 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 from a similar perspective.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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. https://projecteuclid.org/euclid.agt/1513715309