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Mathematics, Geometric Topology
Abstract:
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 $F_0$ and $F_1$ are
such surfaces in a 4-manifold $X$ that are homotopic and there exists an
immersed framed 2-sphere $G$ in $X$ intersecting $F_0$ geometrically once, then
$F_0$ and $F_1$ are concordant if and only if their Freedman-Quinn invariant
$\mathop{fq}$ vanishes. The proof of the main result involves computing
$\mathop{fq}$ in terms of intersections in the universal covering space and
then applying work of Sunukjian in the simply-connected case.
