Show simple item record

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.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2015-16
local.scientificprogramResearch in Pairs 2014
local.series.idOWP-2015-16
dc.identifier.urnurn:nbn:de:101:1-201511175727
dc.identifier.ppn1658875915


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record