Embedding surfaces in 4–manifolds

Kasprowski, Daniel¹ ; Powell, Mark² ; Ray, Arunima³ ; Teichner, Peter³

¹ School of Mathematical Sciences, University of Southampton, Southampton, United Kingdom
² School of Mathematics and Statistics, University of Glasgow, Glasgow, United Kingdom
³ Max Planck Institute for Mathematics, Bonn, Germany

Geometry & topology, Tome 28 (2024) no. 5, pp. 2399-2482.

Résumé

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.

Détail

DOI : 10.2140/gt.2024.28.2399

Keywords: embedding surfaces in 4–manifolds, Kervaire–Milnor invariant

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