Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Embedding 3-manifolds in spin 4-manifolds   An invariant of orientable 3-manifolds is defined by taking the minimum $n$
such that a given 3-manifold embeds in the connected sum of $n$ copies of $S^2
\times S^2$, and we call this $n$ the embedding number of the 3-manifold. We
give some general properties of this invariant, and make calculations for
families of lens spaces and Brieskorn spheres. We show how to construct
rational and integral homology spheres whose embedding numbers grow arbitrarily
large, and which can be calculated exactly if we assume the 11/8-Conjecture. In
a different direction we show that any simply connected 4-manifold can be split
along a rational homology sphere into a positive definite piece and a negative
definite piece.

7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn