Y‐meshes and generalized pentagram maps. Issue 4 (7th March 2016)

• Record Type: Journal Article
• Authors: Glick, Max; Pylyavskyy, Pavlo
• Is Part Of: Proceedings of the London Mathematical Society. Volume 112:Issue 4(2016:Apr.)
• Page Start: 753
• Page End: 797
• Publication Date: 2016-03-07
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1112/plms/pdw007
• Languages: English
• ISSNs: 0024-6115

Abstract

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 asY ‐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.