Concordance of surfaces in 4-manifolds and the Freedman-Quinn invariant

摘要

We prove a concordance version of the 4-dimensional light bulb theorem for pi 1-negligible compact orientable surfaces, where there is a framed but not necessarily embedded dual sphere. That is, we show that if F0 and F1 are such surfaces in a 4-manifold X that are homotopic and there exists an immersed framed 2-sphere G in X intersecting F0 geometrically once, then F0 and F1 are concordant if and only if their Freedman-Quinn invariant fq vanishes. The proof of the main result involves computing fq in terms of intersections in the universal covering space and then applying work of Sunukjian in the simply-connected case. This paper relies extensively on colour figures. Some references to colour may not be meaningful in the printed version, and we refer the reader to the online version which includes the colour figures.