Links Of Surface Singularities Research Articles

Heegaard Floer invariants of contact structures on links of surface singularities

Let a contact 3-manifold (Y, \xi_0) be the link of a normal surface singularity equipped with its canonical contact structure \xi_0 . We prove a special property of such contact 3-manifolds of "algebraic" origin: the Heegaard Floer invariant c^+(\xi_0)\in \mathrm {HF}^+(-Y) cannot lie in the image of the U -action on \mathrm {HF}^+(-Y) . It follows that Karakurt's "height of U -tower" invariants are always 0 for canonical contact structures on singularity links, which contrasts the fact that the height of U -tower can be arbitrary for general fillable contact structures. Our proof uses the interplay between the Heegaard Floer homology and Némethi's lattice cohomology.

Links of surface singularities and CR space forms

We classify 3-dimensional compact locally homogeneous non-degenerate CR-manifolds (“CR space-forms”). Most of them are links of normal complex surface singularities, and we classify these singularities.