Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Analysis of the Representations of the Mapping Class Group of a
  Multi-Geon Three-Manifold   It is well known that the inequivalent unitary irreducible representations
(UIR's) of the mapping class group $G$ of a 3-manifold give rise to ``theta
sectors'' in theories of quantum gravity with fixed spatial topology. In this
paper, we study several families of UIR's of $G$ and attempt to understand the
physical implications of the resulting quantum sectors. The mapping class group
of a three-manifold which is the connected sum of $\R^3$ with a finite number
of identical irreducible primes is a semi-direct product group. Following
Mackey's theory of induced representations, we provide an analysis of the
structure of the general finite dimensional UIR of such a group. In the picture
of quantized primes as particles (topological geons), this general
group-theoretic analysis enables one to draw several interesting qualitative
conclusions about the geons' behavior in different quantum sectors, without
requiring an explicit knowledge of the UIR's corresponding to the individual
primes.

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The categories of this paper are: math
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
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The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio