Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite groups, spherical 2-categories, and 4-manifold invariants   In this paper we define a class of state-sum invariants of compact closed
oriented piece-wise linear 4-manifolds using finite groups. The definition of
these state-sums follows from the general abstract construction of 4-manifold
invariants using spherical 2-categories, as we defined in a previous paper,
although it requires a slight generalization of that construction. We show that
the state-sum invariants of Birmingham and Rakowski, who studied
Dijkgraaf-Witten type invariants in dimension 4, are special examples of the
general construction that we present in this paper. They showed that their
invariants are non-trivial by some explicit computations, so our construction
includes interesting examples already. Finally, we indicate how our
construction is related to homotopy 3-types. This connection suggests that
there are many more interesting examples of our construction to be found in the
work on homotopy 3-types, such as by Brown, for example.

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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess