Y-meshes and generalized pentagram maps

Max Glick, Pavlo Pylyavskyy

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

We introduce a rich family of generalizations of the pentagram map sharing the property that each generates an infinite configuration of points and lines with four points on each line. These systems all have a description as Y-mutations in a cluster algebra and hence establish new connections between cluster theory and projective geometry. Our framework incorporates many preexisting generalized pentagram maps due to M. Gekhtman, M. Shapiro, S. Tabachnikov, and A. Vainshtein and also B. Khesin and F. Soloviev. In several of these cases a reduction to cluster dynamics was not previously known.

Original languageEnglish (US)
Pages (from-to)753-797
Number of pages45
JournalProceedings of the London Mathematical Society
Volume112
Issue number4
DOIs
StatePublished - Apr 1 2016

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