Representation varieties of Fuchsian groups
Michael Larsen, Alexander Lubotzky
TL;DR
This paper estimates the dimension of representation varieties of Fuchsian groups into simple real algebraic groups, addressing a specific open question and advancing understanding of these algebraic structures.
Contribution
It provides new dimension estimates for Hom(F,G) where F is a Fuchsian group and G is a simple real algebraic group, answering a question posed by Dolgachev.
Findings
Dimension estimates for Hom(F,G) varieties.
Resolution of Dolgachev's question.
Enhanced understanding of Fuchsian group representations.
Abstract
We estimate the dimension of varieties of the form Hom(F,G) where F is a Fuchsian group and G is a simple real algebraic group, answering along the way a question of I. Dolgachev.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Advanced Combinatorial Mathematics