Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chain flaring and $L^{2}$-torsion of free-by-cyclic groups   We introduce a condition on the monodromy of a free-by-cyclic group,
$G_\phi$, called the chain flare condition, that implies that the
$L^2$-torsion, $\rho^{(2)}(G_\phi)$, is non-zero. We conjecture that this
condition holds whenever the monodromy is exponentially growing.

18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga