Local invariants of framed fronts in 3-manifolds
The authors deal with front invariants whose increments in generic homotopies are determined entirely by diffeomorphism types of local bifurcations of the fronts. Such invariants are dual to trivial 1-cycles supported on the discriminant in the space of the corresponding Legendrian maps. They describe the space of discriminantal cycles (possibly non-trivial) for framed fronts in an arbitrary oriented 3-manifold, both for the integer and mod-2 coefficients. For most of these cycles the homotopy-independent interpretations are found which guarantee the triviality required. In particular, the authors prove that all integer local invariants of Legendrian maps without corank-2 points are essentially exhausted by the number of points of isolated singularity types of the fronts.
scientific article; zbMATH DE number 6489370