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OverviewFor any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, the authors construct a geometric realization in terms of suitable decorated Teichmuller space of the surface. On the geometric side, this requires opening the surface at each interior marked point into an additional geodesic boundary component. On the algebraic side, it relies on the notion of a non-normalized cluster algebra and the machinery of tropical lambda lengths. The authors' model allows for an arbitrary choice of coefficients which translates into a choice of a family of integral laminations on the surface. It provides an intrinsic interpretation of cluster variables as renormalized lambda lengths of arcs on the surface. Exchange relations are written in terms of the shear coordinates of the laminations and are interpreted as generalized Ptolemy relations for lambda lengths. This approach gives alternative proofs for the main structural results from the authors' previous paper, removing unnecessary assumptions on the surface. Full Product DetailsAuthor: Sergey Fomin , Dylan ThurstonPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.173kg ISBN: 9781470429676ISBN 10: 1470429675 Pages: 101 Publication Date: 30 October 2018 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Temporarily unavailable The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Table of ContentsReviewsAuthor InformationSergey Fomin, University of Michigan, Ann Arbor, MI. Dylan Thurston, Indiana University, Bloomington, IN. Tab Content 6Author Website:Countries AvailableAll regions |