Fock–Goncharov coordinates for semisimple Lie groups

dc.contributor.advisor	Zickert, Christian	en_US
dc.contributor.author	Gilles, S	en_US
dc.contributor.department	Mathematics	en_US
dc.contributor.publisher	Digital Repository at the University of Maryland	en_US
dc.contributor.publisher	University of Maryland (College Park, Md.)	en_US
dc.date.accessioned	2021-07-07T05:47:43Z
dc.date.available	2021-07-07T05:47:43Z
dc.date.issued	2021	en_US
dc.description.abstract	Fock and Goncharov introduced cluster ensembles, providing a framework for coordinates on varieties of surface representations into Lie groups, as well as a complete construction for groups of type $A_n$. Later, Zickert, Le , and Ip described, using differing methods, how to apply this framework for other Lie group types. Zickert also showed that this framework applies to triangulated $3$-manifolds. We present a complete, general construction, based on work of Fomin and Zelevinsky. In particular, we complete the picture for the remaining cases: Lie groups of types $F_4$, $E_6$, $E_7$, and $E_8$.	en_US
dc.identifier	https://doi.org/10.13016/2ihm-x8ls
dc.identifier.uri	http://hdl.handle.net/1903/27312
dc.language.iso	en	en_US
dc.subject.pqcontrolled	Mathematics	en_US
dc.title	Fock–Goncharov coordinates for semisimple Lie groups	en_US
dc.type	Dissertation	en_US

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