Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Box spaces of the free group that neither contain expanders nor embed
  into a Hilbert space   We construct box spaces of a free group that do not coarsely embed into a
Hilbert space, but do not contain coarsely embedded expanders. We do this by
considering two sequences of subgroups of the free group: one which gives rise
to a box space which forms an expander, and another which gives rise to a box
space that can be coarsely embedded into a Hilbert space. We then take certain
intersections of these subgroups, and prove that the corresponding box space
contains generalized expanders. We show that there are no coarsely embedded
expanders in the box space corresponding to our chosen sequence by proving that
a box space that covers another box space of the same group that is coarsely
embeddable into a Hilbert space cannot contain coarsely embedded expanders.

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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: nlin