Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Negative curvature in graphical small cancellation groups   We use the interplay between combinatorial and coarse geometric versions of
negative curvature to investigate the geometry of infinitely presented
graphical $Gr'(1/6)$ small cancellation groups. In particular, we characterize
their 'contracting geodesics', which should be thought of as the geodesics that
behave hyperbolically.
  We show that every degree of contraction can be achieved by a geodesic in a
finitely generated group. We construct the first example of a finitely
generated group $G$ containing an element $g$ that is strongly contracting with
respect to one finite generating set of $G$ and not strongly contracting with
respect to another. In the case of classical $C'(1/6)$ small cancellation
groups we give complete characterizations of geodesics that are Morse and that
are strongly contracting.
  We show that many graphical $Gr'(1/6)$ small cancellation groups contain
strongly contracting elements and, in particular, are growth tight. We
construct uncountably many quasi-isometry classes of finitely generated,
torsion-free groups in which every maximal cyclic subgroup is hyperbolically
embedded. These are the first examples of this kind that are not subgroups of
hyperbolic groups.
  In the course of our analysis we show that if the defining graph of a
graphical $Gr'(1/6)$ small cancellation group has finite components, then the
elements of the group have translation lengths that are rational and bounded
away from zero.

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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph