Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pulling Apart 2-spheres in 4-manifolds   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 S^2\times S^2; 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.

11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org