English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Recovering the topology of surfaces from cluster algebras

MPS-Authors
/persons/resource/persons236470

Yakimov,  Milen
Max Planck Institute for Mathematics, Max Planck Society;

Locator
Fulltext (public)

arXiv:1607.02131.pdf
(Preprint), 353KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Bucher, E., & Yakimov, M. (2018). Recovering the topology of surfaces from cluster algebras. Mathematische Zeitschrift, 288(1-2), 565-594. doi:10.1007/s00209-017-1901-4.


Cite as: http://hdl.handle.net/21.11116/0000-0004-6365-B
Abstract
We present an effective method for recovering the topology of a bordered oriented surface with marked points from its cluster algebra. The information is extracted from the maximal triangulations of the surface, those that have exchange quivers with maximal number of arrows in the mutation class. The method gives new proofs of the automorphism and isomorphism problems for the surface cluster algebras as well as the uniqueness of the Fomin–Shapiro–Thurston block decompositions of the exchange quivers of the surface cluster algebras. The previous proofs of these results followed a different approach based on Gu’s direct proof of the last result. The method also explains the exceptions to these results due to pathological problems with the maximal triangulations of several surfaces.