Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solvable groups and a shear construction   The twist construction is a geometric model of T-duality that includes
constructions of nilmanifolds from tori. This paper shows how one-dimensional
foliations on manifolds may be used in a shear construction, which in algebraic
form builds certain solvable Lie groups from Abelian ones. We discuss other
examples of geometric structures that may be obtained from the shear
construction.

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The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin