All knots in $R^3$ possess Seifert surfaces, and so the classical Thurston-Bennequin and rotation (or Maslov) invariants for Legendrian knots in a contact structure on $R^3$ can be defined. The definitions extend easily to null-homologous knots in an
y $3$-manifold $M$ endowed with a contact structure $xi$. We generalize the definition of Seifert surfaces and use them to define these invariants for all Legendrian knots, including those that are not null-homologous, in a contact structure on the $3$-torus $T^3$. We show how to compute the Thurston-Bennequin and rotation invariants in a tight oriented contact structure on $T^3$ using projections.
We present new open manifolds that are not homeomorphic to leaves of any C^0 codimension one foliation of a compact manifold. Among them are simply connected manifolds of dimension 5 or greater that are non-periodic in homotopy or homology, namely in their 2-dimensional homotopy or homology groups.
