Tue, June 10, 2014
3:00 pm - 4:00 pm
MW154
Title: Lattice and Heegaard - Floer homologies of algebraic links
Speaker: András Némethi, Alfréd Rényi of Mathematics, Budapest
Abstract: We compute the Heegaard-Floer link homology of algebraic links in terms of the multivariate Hilbert function of the corresponding plane curve singularities. A new version of lattice homology is defined: the lattice corresponds to the normalization of the singular germ, and the Hilbert function serves as the weight function. The main result of the paper identifies four homologies:
- the lattice homology associated with the Hilbert function,
- the homologies of the projectivized complements of local hyperplane arrangements cut out from the local algebra by valuations given by the normalizations of irreducible components,
- a certain variant of the Orlik--Solomon algebra of these local arrangements, and
- the Heegaard--Floer link homology of the local embedded link of the germ.
In particular, the Poincar'e polynomials of all these homology groups are the same, and we also show that they agree with the coefficients of the motivic Poincar'e series of the singularity.