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Cluster algebras and triangulated surfaces. Part II: Lambda lengths

Author: Sergey Fomin; Dylan P Thurston
Publisher: Providence, RI : American Mathematical Society, [2018] ©2018
Series: Memoirs of the American Mathematical Society, no. 1223.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
"For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, we construct a geometric realization in terms of suitable decorated Teichmüller 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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
(DLC) 2018040837
(OCoLC)1055759265
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Sergey Fomin; Dylan P Thurston
ISBN: 1470448238 9781470448233
OCLC Number: 1056194025
Notes: "September 2018, volume 255, number 1223 (sixth of 7 numbers)."
Keywords:Cluster algebra, lambda length, decorated Teichmüller space, opened surface, tagged triangulation, shear coordinates, integral lamination, Ptolemy relations
Part 1 was issued as S. Fomin, M. Shapiro, and D. Thurston, Cluster algebras and triangulated surfaces. I. Cluster complexes, Acta Math. 201 (2008), no. 1, 83-146, DOI 10.1007/s11511-008-0030-7. MR2448067.--Page 95.
Description: 1 online resource (v, 95 pages) : illustrations.
Contents: IntroductionNon-normalized cluster algebrasRescaling and normalizationCluster algebras of geometric type and their positive realizationsBordered surfaces, arc complexes, and tagged arcsStructural resultsLambda lengths on bordered surfaces with puncturesLambda lengths of tagged arcsOpened surfacesLambda lengths on opened surfacesNon-normalized exchange patterns from surfacesLaminations and shear coordinatesShear coordinates with respect to tagged triangulationsTropical lambda lengthsLaminated Teichmuller spacesTopological realizations of some coordinate ringsPrincipal and universal coefficientsAppendix A. Tropical degeneration and relative lambda lengthsAppendix B. Versions of Teichmuller spaces and coordinatesBibliography
Series Title: Memoirs of the American Mathematical Society, no. 1223.
Responsibility: Sergey Fomin, Dylan Thurston.

Abstract:

For 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  Read more...

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