CEU Electronic Theses and Dissertations, 2013
| Author | László, Tamás |
|---|---|
| Title | Lattice cohomology and Seiberg-Witten invariants of normal surface singularities |
| Summary | One of the main questions in the theory of normal surface singularities is to understand the relations between their geometry and topology. The lattice cohomology is an important tool in the study of topological properties of a plumbed 3-manifold M associated with a connected negative denite plumbing graph G. It connects the topological properties with analytic ones when M is realized as a singularity link, i.e. when G is a good resolution graph of the singularity. Its computation is based on the (Riemann-Roch) weights of lattice points. The first part of the thesis reduces the rank of this lattice to the number of `bad' vertices of the graph. Usually, the geometry/topology of M is codified exactly by these `bad' vertices and their number measures how far the plumbing graph stays from a rational one. In the second part, we identify the following three objects: the Seiberg-Witten invariant of a plumbed 3-manifold, the periodic constant of its topological Poincare series, and a coeficient of an equivariant multivariable Ehrhart polynomial. We end the thesis with detailed calculations and examples. |
| Supervisor | Némethi, András |
| Department | Mathematics PhD |
| Full text | https://www.etd.ceu.edu/2013/laszlo_tamas.pdf |
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