Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinite series of quaternionic 1-vertex cube complexes, the doubling
  construction, and explicit cubical Ramanujan complexes   We construct vertex transitive lattices on products of trees of arbitrary
dimension $d \geq 1$ based on quaternion algebras over global fields with
exactly two ramified places. Starting from arithmetic examples, we find
non-residually finite groups generalizing earlier results of Wise, Burger and
Mozes to higher dimension. We make effective use of the combinatorial language
of cubical sets and the doubling construction generalized to arbitrary
dimension. Congruence subgroups of these quaternion lattices yield explicit
cubical Ramanujan complexes, a higher dimensional cubical version of Ramanujan
graphs (optimal expanders).

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The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
16
The categories of this paper are: stat
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The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg