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|a 1470448238
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|a 9781470448233
|q (electronic bk.)
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|a (OCoLC)1056194025
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|b eng
|e rda
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|d UIU
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|d N$T
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|a CODA
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| 050 |
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4 |
|a QA251.3
|b .F66 2018
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| 072 |
|
7 |
|a MAT
|x 002040
|2 bisacsh
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| 100 |
1 |
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|a Fomin, Sergey,
|e author.
|0 http://id.loc.gov/authorities/names/nb2002072966.
|
| 245 |
1 |
0 |
|a Cluster algebras and triangulated surfaces.
|n Part II,
|p Lambda lengths /
|c Sergey Fomin, Dylan Thurston.
|
| 264 |
|
1 |
|a Providence, RI :
|b American Mathematical Society,
|c [2018]
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| 264 |
|
4 |
|c ©2018.
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| 300 |
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|a 1 online resource (v, 95 pages) :
|b illustrations.
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| 336 |
|
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|a text
|b txt
|2 rdacontent.
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| 337 |
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|a computer
|b c
|2 rdamedia.
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| 338 |
|
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|a online resource
|b cr
|2 rdacarrier.
|
| 490 |
1 |
|
|a Memoirs of the American Mathematical Society,
|x 0065-9266 ;
|v number 1223.
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| 500 |
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|a "September 2018, volume 255, number 1223 (sixth of 7 numbers)."
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| 500 |
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|a Keywords:Cluster algebra, lambda length, decorated Teichmüller space, opened surface, tagged triangulation, shear coordinates, integral lamination, Ptolemy relations.
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| 504 |
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|a Includes bibliographical references (pages 95-97)
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| 500 |
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|a Part 1 was issued as S. Fomin, M. Shapiro, and D. Thurston, Cluster algebras and triangulated surfaces. I. Cluster complexes, Acta Math. 201 (2008), number 1, 83-146, DOI 10.1007/s11511-008-0030-7. MR2448067.--Page 95.
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| 520 |
3 |
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|a "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 non-normalized cluster algebra and the machinery of tropical lambda lengths. Our 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 our previous paper, removing unnecessary assumptions on the surface."--Page v.
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| 588 |
0 |
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|a Print version record.
|
| 650 |
|
0 |
|a Cluster algebras.
|0 http://id.loc.gov/authorities/subjects/sh2010012666.
|
| 650 |
|
0 |
|a Lambda algebra.
|0 http://id.loc.gov/authorities/subjects/sh85074173.
|
| 650 |
|
0 |
|a Teichmüller spaces.
|0 http://id.loc.gov/authorities/subjects/sh85133253.
|
| 650 |
|
7 |
|a Cluster algebras.
|2 fast
|0 (OCoLC)fst01763173.
|
| 650 |
|
7 |
|a Lambda algebra.
|2 fast
|0 (OCoLC)fst00991009.
|
| 650 |
|
7 |
|a Teichmüller spaces.
|2 fast
|0 (OCoLC)fst01145803.
|
| 700 |
1 |
|
|a Thurston, Dylan P.,
|d 1972-
|e author.
|0 http://id.loc.gov/authorities/names/n2018036039.
|
| 776 |
0 |
8 |
|i Print version:
|z 9781470429676
|w (DLC) 2018040837
|w (OCoLC)1055759265.
|
| 856 |
4 |
0 |
|z Online Access
|u https://colorado.idm.oclc.org/login?url=http://www.ams.org/books/memo/1223/memo1223.pdf
|
| 830 |
|
0 |
|a Memoirs of the American Mathematical Society ;
|v no. 1223.
|0 http://id.loc.gov/authorities/names/n83703151.
|
| 907 |
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|a .b103137634
|b 03-08-23
|c 01-28-19
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|b 02-04-19
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| 952 |
f |
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|p Can circulate
|a University of Colorado Boulder
|b Online
|c Online
|d Online
|e QA251.3 .F66 2018
|h Library of Congress classification
|i web
|n 1
|
