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Conjugating Representations into Lie...

Miller, Jared Tristan.

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Conjugating Representations into Lie Subgroups.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Conjugating Representations into Lie Subgroups./
Author:	Miller, Jared Tristan.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2024,
Description:	116 p.
Notes:	Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
Contained By:	Dissertations Abstracts International85-12B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30994512
ISBN:	9798382786698

Conjugating Representations into Lie Subgroups.
Miller, Jared Tristan.

Conjugating Representations into Lie Subgroups. - Ann Arbor : ProQuest Dissertations & Theses, 2024 - 116 p.

Source: Dissertations Abstracts International, Volume: 85-12, Section: B.

Thesis (Ph.D.)--The Florida State University, 2024.

Properties of the space of representations of a surface group into a given simple Lie group is a very active area of research and is particularly relevant to higher Teichmuller theory. For a closed surface, classical Teichmuller space is a connected component of the moduli space of representations into PSL2(R) and showed that the space of positive representations into PSLk(R) coincides with the Hitchin component. In this dissertation we study representations of finitely generated groups into PGLk(C) and determine necessary and sufficient conditions for such a representation to be conjugate into PGLk(R). In this way, we identify representations in the larger representation variety which are conjugate in PGLk(C) to a representation in hom π1(Σ), PGLk(R)) /PGLk(R).

ISBN: 9798382786698Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Fock-Goncharov

Conjugating Representations into Lie Subgroups.
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020 $a 9798382786698
035 $a (MiAaPQ)AAI30994512
035 $a AAI30994512
040 $a MiAaPQ $c MiAaPQ
100 1 $a Miller, Jared Tristan. $0 (orcid)0009-0004-6743-4679 $3 3769933
245 1 0 $a Conjugating Representations into Lie Subgroups.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2024
300 $a 116 p.
500 $a Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
500 $a Advisor: Ballas, Samuel.
502 $a Thesis (Ph.D.)--The Florida State University, 2024.
520 $a Properties of the space of representations of a surface group into a given simple Lie group is a very active area of research and is particularly relevant to higher Teichmuller theory. For a closed surface, classical Teichmuller space is a connected component of the moduli space of representations into PSL2(R) and showed that the space of positive representations into PSLk(R) coincides with the Hitchin component. In this dissertation we study representations of finitely generated groups into PGLk(C) and determine necessary and sufficient conditions for such a representation to be conjugate into PGLk(R). In this way, we identify representations in the larger representation variety which are conjugate in PGLk(C) to a representation in hom π1(Σ), PGLk(R)) /PGLk(R).
590 $a School code: 0071.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Fock-Goncharov
653 $a Geometry
653 $a Lie groups
653 $a Projective space
653 $a Projective transformations
653 $a Topology
690 $a 0405
690 $a 0642
710 2 $a The Florida State University. $b Mathematics. $3 2095897
773 0 $t Dissertations Abstracts International $g 85-12B.
790 $a 0071
791 $a Ph.D.
792 $a 2024
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30994512