Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-splittability of the rational homology cobordism group of
  3-manifolds   The smooth rational homology cobordism group of rational homology three
spheres, T, contains subgroups T_p generated by 3-manifolds with first homology
p-torsion, where p is a prime. Rochlin's theorem and gauge theoretic methods
show that the inclusion of the direct sum of the T_p into T has infinitely
generated kernel. We use Heegaard-Floer methods to show that the cokernel is
infinitely generated. On the level of Witt groups of linking forms and
conjecturally in the topological category, the inclusion is an isomorphism.
  One application is the demonstration of the failure in dimension three of an
algebraic and higher dimensional theorem of Stoltzfus regarding primary
splittings in the knot concordance group. We also build on work of the second
author with Hedden and Ruberman to prove that the homology cobordism group of
rational homology three spheres that bound topological rational homology
4-balls remains infinitely generated when modded out by the homology cobordism
group of integral homology 3-spheres.

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The categories of this paper are: eess
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The categories of this paper are: econ
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
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The categories of this paper are: ao-sci