Embedding surfaces in 4-manifolds

Abstract

We prove a surface embedding theorem for 4-manifolds with good fundamental group in the presence of dual spheres, with no restriction on the normal bundles. The new obstruction is a Kervaire-Milnor invariant for surfaces and we give a combinatorial formula for its computation. For this we introduce the notion of band characteristic surfaces.

56 pages, 20 figures; in v2, we have added a new section (Section 1.5) containing applications to knot theory; v3: several minor changes and corrections following a referee report, to appear in Geometry & Topology