Pulling apart 2-spheres in 4-manifolds

Hybrid.
Contact: Christian Kaiser (kaiser@mpim-bonn.mpg.de)

In dimension four, controlling intersections among half-dimensional submanifolds is notoriously difficult.

This talk will describe an obstruction theory for determining whether the connected components of an immersed surface in a 4-manifold can be made pairwise disjoint by a homotopy ('pulled apart'). The corresponding 'higher-order' invariants are defined in terms of decorated unitrivalent trees associated to iterated towers of Whitney disks, and generalize Milnor’s classical link homotopy invariants. Sample results include that in an arbitrary simply connected 4-manifold any number of parallel copies of an immersed 2-sphere with vanishing self-intersection number can be pulled apart, and that this is not always true in the non-simply connected setting.