Invariance of Knot Lattice Homotopy

Contact: Aru Ray (aruray @ mpim-bonn.mpg.de)

Links of singularity and generalized algebraic links are ways of constructing three-manifolds and smooth links inside them from algebraic surfaces and curves inside them. Némethi created lattice homology as an invariant for links of normal surface singularities which developed out of computations for Heegaard Floer homology. Later Ozsváth, Stipsicz, and Szabó defined knot lattice homology for generalized algebraic knots. I discuss a proof that the filtered knot lattice space is an invariant of the smooth knot type, which had been previously suspected but not confirmed. At the end I give a hint toward current work to make this invariant more computable.