Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cutting sequences on square-tiled surfaces   We characterize cutting sequences of infinite geodesics on square-tiled
surfaces by considering interval exchanges on specially chosen intervals on the
surface. These interval exchanges can be thought of as skew products over a
rotation, and we convert cutting sequences to symbolic trajectories of these
interval exchanges to show that special types of combinatorial lifts of
Sturmian sequences completely describe all cutting sequences on a square-tiled
surface. Our results extend the list of families of surfaces where cutting
sequences are understood to a dense subset of the moduli space of all
translation surfaces.

19
The categories of this paper are: eess
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The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
3
The categories of this paper are: physics