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- W2310448326 abstract "An invariant is a quantity which remains unchanged under certain classes of transformations. A wave front (or a front) in a 3-manifold is the image of a surface under a Legendrian map. The aim of this thesis is the description of all local invariants of fronts in 3-manifolds. The front invariants under consideration are those whose increments in generic homotopies are determined entirely by diffeomorphism types of local bifurcations of the fronts. Such invariants are dual to trivial codimension 1 cycles supported on the discriminant in the space of corresponding Legendrian maps. We describe the spaces of the discriminantal cycles (possibly non-trivial) for various orientation and co-orientation settings of the fronts in an arbitrary oriented 3-manifold, both for the integer and mod2 coefficients. For the majority of these cycles we find homotopy-independent interpretations which guarantee the triviality required. In particular, in the case of framed fronts we show that all integer local invariants of Legendrian maps without corank 2 points are essentially exhausted by the numbers of points of isolated singularity types of the fronts." @default.
- W2310448326 created "2016-06-24" @default.
- W2310448326 creator A5019191391 @default.
- W2310448326 date "2014-11-01" @default.
- W2310448326 modified "2023-09-23" @default.
- W2310448326 title "Local invariants of fronts in 3-manifolds" @default.
- W2310448326 doi "https://doi.org/10.17638/02006756" @default.
- W2310448326 hasPublicationYear "2014" @default.
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