Knotted Legendrian surfaces with few Reeb chords
2011 (English)In: Algebraic and Geometric Topology, ISSN 1472-2747, E-ISSN 1472-2739, Vol. 11, no 5, 2903-2936 p.Article in journal (Refereed) Published
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(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 J(1)(S-2) from a similar perspective.
Place, publisher, year, edition, pages
2011. Vol. 11, no 5, 2903-2936 p.
IdentifiersURN: urn:nbn:se:uu:diva-172252DOI: 10.2140/agt.2011.11.2903ISI: 000299576600013OAI: oai:DiVA.org:uu-172252DiVA: diva2:513911