CEU Electronic Theses and Dissertations, 2011
| Author | Komuves, Balazs |
|---|---|
| Title | On computing Thom polynomials |
| Summary | The subject matter of this thesis is the computation of Thom polynomials of singularities of maps, in particular Thom-Boardman singularity classes. A "singularity" means a type of local behaviour of maps between smooth (or analytic) manifolds; the simplest example is the differential being degenerate. It is well known that the cohomology class of the (closure of the) locus in the source manifold where a map has a given singularity can be expressed as a polynomial of the characteristic classes of the map. This multivariate polynomial, which only depends on the singularity and the dimensions, is called the Thom polynomial of the singularity. Even though the above phenomenon was observed by Thom more than 50 years ago, there are still only a few examples where we can explicitly calculate these polynomials. In this work, we contribute both new methods of computations, and explicit calculations of some previously unknown Thom polynomials. In particular, we discover a connection between localization formulae for contact singularities and basic hypergeometric series; we present a new geometric construction to compactify some moduli spaces related to Thom-Boardman classes; and we give new formulae for the Thom polynomials of some second order Thom-Boardman singularities. |
| Supervisor | Feher, Laszlo |
| Department | Mathematics PhD |
| Full text | https://www.etd.ceu.edu/2011/tphkob01.pdf |
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