Concordance of surfaces in 4‐manifolds and the Freedman–Quinn invariant. Issue 2 (10th May 2021)

• Record Type: Journal Article
• Authors: Klug, Michael R.; Miller, Maggie
• Is Part Of: Journal of topology. Volume 14:Issue 2(2021)
• Page Start: 560
• Page End: 586
• Publication Date: 2021-05-10
• Subjects: 57K45 (primary) -- 57K40 (secondry); Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12191
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract: We prove a concordance version of the 4‐dimensional light bulb theorem for π 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 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.