Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The outside of the Teichmuller space of punctured tori in Maskit's
  embedding   We consider the following question: Which parameters in the extension of a
rational pleating ray across the boundary of $\Cal M$, the Maskit embedding of
the Teichm\"uller space of once punctured tori correspond to a Kleinian group?
Using methods of Keen and Series and Wright we prove a local result, stating
that on each rational ray there is a sequence of parameters in $\overline\Bbb
H\setminus\Cal M$ accumulating at the boundary point of $\Cal M$ on the ray.
These are the unique parameters on the extended $p/q$ ray for which the special
word $W_{p/q}$ is a primitive elliptic M\"obius transformation. We also show
that the discrete groups with elliptic elements in the complement of
$\overline{\Cal M}$ are boundary groups of deformation spaces of certain
Kleinian groups representing a punctured torus on their invariant component.

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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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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: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th