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Cluster Algebras and Triangulated Surfaces Part II Lambda Lengths Sergey Fomin
Cluster Algebras and Triangulated Surfaces Part II Lambda Lengths


    Book Details:

  • Author: Sergey Fomin
  • Published Date: 30 Oct 2018
  • Publisher: American Mathematical Society
  • Language: English
  • Format: Paperback::101 pages
  • ISBN10: 1470429675
  • Publication City/Country: Providence, United States
  • File name: Cluster-Algebras-and-Triangulated-Surfaces-Part-II-Lambda-Lengths.pdf
  • Dimension: 178x 254mm
    • Download: Cluster Algebras and Triangulated Surfaces Part II Lambda Lengths


CLUSTER ALGEBRAS AND TRIANGULATED SURFACES PART II: LAMBDA LENGTHS SERGEY FOMIN AND DYLAN THURSTON Abstract. We construct geometric models for cluster algebras associated with bordered surfaces with marked points, for any choice of coe cients of geometric type, using generalized decorated Teichm uller spaces. In this context, the cluster 4 Triangulated surfaces. 5 Result. 2 / 17. Page 3. Notations. A:a finite dimensional algebra over a field k. Triangulated surfaces Part I: Cluster complexes, Acta. Part II: Lambda lengths, Memoirs AMS, 255(1223) 2018. Vector calculus, linear algebra, and differential forms:a unified approach. - 5th ed. Ithaca Cluster algebras and triangulated surfaces. Part II: lambda lengths Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths: New copy - Usually dispatched within 2 working days. Bases for cluster algebras from surfaces - Volume 149 Issue 2 - Gregg Musiker, Ralf Schiffler, Lauren Williams Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Part of the CRM Short Courses book series (CRMSC) Abstract. Cluster Teichmüller theory (lambda-lengths, Penner coordinates, cluster varieties) Knot theory (Chern Simons invariants, volume conjecture, Legendrian knots) Thurston, D.: Cluster algebras and triangulated surfaces. I. Cluster complexes. Acta Math. 201(1), 83 146 (2008). CLUSTER ALGEBRAS AND TRIANGULATED SURFACES II 5 Teichmu ller space. In Section 10, we show that suitably rescaled lambda lengths of lifted arcs form a non-normalized exchange pattern, providing a crucial building block for our main construction (to be completed in Section 14). 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. Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths English | 2018 | ISBN: 1470429675 | 110 Pages | PDF | 1.45 MB Sergey Fomin and D. Keywords: cyclic polytopes, triangulation, bistellar flip, cluster algebra, Cluster algebras and triangulated surfaces. Part II: Lambda lengths. Preprint, 2008. The Mathematics Department (D-MATH) is responsible for Mathematics instruction in all programs of study at the ETHZ. For students concentrating in Mathematics, the Department offers a rich and carefully coordinated program of courses and seminars in a broad range of fields of pure and applied mathematics. The curriculum is designed to acquaint students with fundamental mathematical Our main result is Theorem 2, a definition of snake graphs from orbifolds that gives of cluster algebras associated with triangulated surfaces [6, 7], Felikson, Shapiro, In this section, we briefly review some nomenclature and (S, M); and (3) the cluster variable xγ corresponding to arc is given the lambda length of. Cluster algebras and triangulated surfaces. Part II: Lambda lengths. For any cluster algebra whose underlying combinatorial data can be encoded a bordered surface with marked points, we construct a geometric realization in terms of suitable decorated Teichmueller space of the surface. Wonder of sine-Gordon -systems. Authors: Tomoki Nakanishi and Salvatore Stella Journal: Trans. Amer. Math. Soc. 368 (2016), 6835-6886 MSC (2010): Primary 13F60, 17B37 Greedy Bases in Rank 2 Quantum Cluster Algebras. A famous conjecture of Fomin and Zelevinsky [recently proved Cerulli Irelli et al. For a large class of cluster algebras called skew symmetric ] states that the cluster monomials form a linear independent subset of a cluster algebra. There has been great interest in the problem of finding Cluster algebras were conceived Fomin and Zelevinsky (1) in the spring of 2000 as a 2 15; Poisson geometry (16 19); Teichmüller theory (20 24); string theory 1 shows an example of a triangulation T, with n = 8. Webs on Surfaces, Rings of Invariants, and Clusters Part II: Lambda lengths. CLUSTER ALGEBRAS AND TRIANGULATED SURFACES 5 classes. Some examples of this kind (e.g., finite and affine types E 6 through E 8, Grassmannians Gr 3,9 and Gr 4,8) do not come from triangulated surfaces. The main result of Section 13 is a purely combinatorial description of the class and Stephen Wainger, Algebras of Singular Integral Operators with Kernels Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths, 2018 Abstract. We study cluster algebras with principal coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of perfect matchings of a certain graph G T, that is constructed from the surface recursive glueing of elementary pieces that we call tiles.





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