2007/10/24 by Tobias Ekholm, Ekholm, Tobias, Tamás Kálmán +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #53D40 #57R17 #Connective tissue disorders research #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.0710.4382
openalex publication_date 2007/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a Legendrian 2-torus in the 1-jet space of S1×\R (or of \R2) from a loop of Legendrian knots in the 1-jet space of \R. The differential graded algebra (DGA) for the Legendrian contact homology of the torus is explicitly computed in terms of the DGA of the knot and the monodromy operator of the loop. The contact homology of the torus is shown to depend only on the chain homotopy type of the monodromy operator. The construction leads to many new examples of Legendrian knotted tori. In particular, it allows us to construct a Legendrian torus with DGA which does not admit any augmentation (linearization) but which still has non-trivial homology, as well as two Legendrian tori with isomorphic linearized contact homologies but with distinct contact homologies.