Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ideal triangulations and geometric transitions   Thurston introduced a technique for finding and deforming three-dimensional
hyperbolic structures by gluing together ideal tetrahedra. We generalize this
technique to study families of geometric structures that transition from
hyperbolic to anti de Sitter (AdS) geometry. Our approach involves solving
Thurston's gluing equations over several different shape parameter algebras. In
the case of a punctured torus bundle with Anosov monodromy, we identify two
components of real solutions for which there are always nearby positively
oriented solutions over both the complex and pseudo-complex numbers. These
complex and pseudo-complex solutions define hyperbolic and AdS structures that,
after coordinate change in the projective model, may be arranged into one
continuous family of real projective structures. We also study the rigidity
properties of certain AdS structures with tachyon singularities.

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The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs