Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cobordism category of plumbed 3-manifolds and intersection product
  structures   In this paper, we introduce a category of graded commutative rings with
certain algebraic morphisms, to investigate the cobordism category of plumbed
3-manifolds. In particular, we define a non-associative distributive algebra
that gives necessary conditions for an abstract morphism between the homologies
of two plumbed 3-manifolds to be realized geometrically by a cobordism. Here we
also consider the homology cobordism monoid, and give a necessary condition
using w-invariants for the homology 3-spheres to belong to the inertia group
associated to some homology 3-spheres.

23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom