On deformations of F n in compact Lie groups

Tsachik Gelander

doi:10.1007/s11856-008-1038-6

On deformations of F _n in compact Lie groups

Tsachik Gelander^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We study some properties of the varieties of deformations of free groups in compact Lie groups. In particular, we prove a conjecture of Margulis and Soifer about the density of non-virtually free points in such variety, and a conjecture of Goldman on the ergodicity of the action of Aut(F _n ) on such variety when n ≥ 3.

Original language	English (US)
Pages (from-to)	15-26
Number of pages	12
Journal	Israel Journal of Mathematics
Volume	167
Issue number	1
DOIs	https://doi.org/10.1007/s11856-008-1038-6
State	Published - Oct 2008

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Mathematics(all)

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abstract = "We study some properties of the varieties of deformations of free groups in compact Lie groups. In particular, we prove a conjecture of Margulis and Soifer about the density of non-virtually free points in such variety, and a conjecture of Goldman on the ergodicity of the action of Aut(F n ) on such variety when n ≥ 3.",

author = "Tsachik Gelander",

note = "Funding Information: ∗The author was partially supported by NSF grant DMS-0404557, BSF grant 2004010, and the {\textquoteright}Finite Structures{\textquoteright} Marie Curie Host Fellowship, carried out at the Alfr{\'e}d R{\'e}nyi Institute of Mathematics in Budapest. Received July 18, 2006 and in revised form February 12, 2007",

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N2 - We study some properties of the varieties of deformations of free groups in compact Lie groups. In particular, we prove a conjecture of Margulis and Soifer about the density of non-virtually free points in such variety, and a conjecture of Goldman on the ergodicity of the action of Aut(F n ) on such variety when n ≥ 3.

AB - We study some properties of the varieties of deformations of free groups in compact Lie groups. In particular, we prove a conjecture of Margulis and Soifer about the density of non-virtually free points in such variety, and a conjecture of Goldman on the ergodicity of the action of Aut(F n ) on such variety when n ≥ 3.

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On deformations of F _n in compact Lie groups

Abstract

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