Legendrian Contact Homology in Seifert Fibered Spaces

摘要

We define a differential graded algebra associated to Legendrian knots inSeifert fibered spaces with transverse contact structures. This construction isdistinguished from other combinatorial realizations of contact homologyinvariants by the existence of orbifold points in the Reeb orbit space of thecontact manifold. These orbifold points are images of the exceptional fibers ofthe Seifert fibered manifold, and they play a key role in the definitions ofthe differential and the grading, as well as the proof of invariance. We applythe invariant to distinguish Legendrian knots whose homology is torsion andwhose underlying topological knot types are isotopic; such examples exist inany sufficiently complicated contact Seifert fibered space.