Frieze patterns, introduced by Coxeter, are infinite arrays of numbers where neighbouring numbers satisfy a local arithmetic rule. Under a certain finiteness assumption, they are in one-to-one correspondence with triangulations of polygons [Conway–Coxeter] and they come from triangulations of annuli in an infinite setting [Baur–Parsons–Tschabold]. In this talk, we will discuss a relationship between pairs of infinite friezes associated with a triangulation of the annulus and explore how one determines the other in an essentially unique way. We will also consider module categories associated with triangulated annuli where infinite friezes may be recovered using a homological formula. This is joint work with Karin Baur, Karin Jacobsen, Maitreyee Kulkarni, and Gordana Todorov.
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