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dc.contributor.authorBerenstein, Arkady
dc.contributor.authorRetakh, Vladimir
dc.date.accessioned2015-11-18T12:00:01Z
dc.date.accessioned2016-10-05T14:14:03Z
dc.date.available2015-11-18T12:00:01Z
dc.date.available2016-10-05T14:14:03Z
dc.date.issued2015-11-18
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1104
dc.descriptionResearch in Pairs 2014en_US
dc.description.abstractThe aim of the paper is to attach a noncommutative cluster-like structure to each marked surface $\Sigma$. This is a noncommutative algebra $\mathcal{A}_\Sigma$ generated by “noncommutative geodesics” between marked points subject to certain triangle relations and noncommutative analogues of Ptolemy-Plücker relations. It turns out that the algebra $\mathcal{A}_\Sigma$ exhibits a noncommutative Laurent Phenomenon with respect to any triangulation of $\Sigma$, which confirms its “cluster nature”. As a surprising byproduct, we obtain a new topological invariant of $\Sigma$, which is a free or a 1-relator group easily computable in terms of any triangulation of $\Sigma$. Another application is the proof of Laurentness and positivity of certain discrete noncommutative integrable systems.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2015,16
dc.titleNoncommutative Marked Surfacesen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2015-16
local.scientificprogramResearch in Pairs 2014
local.series.idOWP-2015-16


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