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Conjugating Representations into Lie Subgroups.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Conjugating Representations into Lie Subgroups./
Author:	Miller, Jared Tristan.
Description:	1 online resource (116 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
Contained By:	Dissertations Abstracts International85-12B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798382786698

Conjugating Representations into Lie Subgroups.
Miller, Jared Tristan.

Conjugating Representations into Lie Subgroups. - 1 online resource (116 pages)

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

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

Includes bibliographical references

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).

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798382786698Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

Fock-GoncharovIndex Terms--Genre/Form:

554714
Electronic books.

Conjugating Representations into Lie Subgroups.
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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).
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538 $a Mode of access: World Wide Web
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653 $a Fock-Goncharov
653 $a Geometry
653 $a Lie groups
653 $a Projective space
653 $a Projective transformations
653 $a Topology
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