Link Homology in 4-Manifolds

Abstract

We define link homology in 4-manifolds, and show that it has a close connection to linking numbers and intersection matrices of 4-manifolds. We also define null-homologous links in 4-manifolds. We give a necessary and sufficient condition for links to be null-homologous in 4-manifolds. This condition implies that for any 4-manifold with second Betti number n, there are (n + 2)-component links which are not nullhomologous in the 4-manifold.