2012/10/19 by Rob Schneiderman, Peter Teichner, Schneiderman, Rob +1
Mathematics · #57M #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M
paper · pdf · doi:10.48550/arxiv.1210.5534
Revised to conform with the published version in Documenta Mathematica
openalex publication_date 2012/10/19 · arxiv created 2015/01/16 · arxiv updated 2015/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
An obstruction theory for representing homotopy classes of surfaces in 4-manifolds by immersions with pairwise disjoint images is developed, using the theory of non-repeating Whitney towers. The accompanying higher-order intersection invariants provide a geometric generalization of Milnor's link-homotopy invariants, and can give the complete obstruction to pulling apart 2-spheres in certain families of 4-manifolds. It is also shown that in an arbitrary simply connected 4-manifold any number of parallel copies of an immersed surface with vanishing self-intersection number can be pulled apart, and that this is not always possible in the non-simply connected setting. The order 1 intersection invariant is shown to be the complete obstruction to pulling apart 2-spheres in any 4-manifold after taking connected sums with finitely many copies of S2× S2; and the order 2 intersection indeterminacies for quadruples of immersed 2-spheres in a simply connected 4-manifold are shown to lead to interesting number theoretic questions.