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Embedding surfaces in 4-manifolds

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arxiv 2201.03961 v3 pith:MDGUCUUC submitted 2022-01-11 math.GT

Daniel Kasprowski , Mark Powell , Arunima Ray , Peter Teichner This is my paper · ORCID
classification math.GT
keywords surfacesembeddingmanifoldsbandbundlescharacteristiccombinatorialcomputation
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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.

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  1. Knotted surfaces with simply-connected complements

    math.GT 2026-07 conditional novelty 6.0 of 10

    Homologous genus-g surfaces with boundary a fixed knot and simply-connected complements in a simply-connected 4-manifold with S^3 boundary are topologically ambiently isotopic rel. boundary.

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