Surjectivity of certain word maps on PSL (2 , C) and SL (2 , C)

Tatiana Bandman; Yuri G. Zarhin

doi:10.1007/s40879-016-0101-9

Surjectivity of certain word maps on PSL (2 , C) and SL (2 , C)

Tatiana Bandman, Yuri G. Zarhin

Department of Mathematics

Pennsylvania State University

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

14 Scopus citations

Abstract

Let n⩾ 2 be an integer and F_n the free group on n generators, [InlineEquation not available: see fulltext.] its first and second derived subgroups. Let K be an algebraically closed field of characteristic zero. We show that if [InlineEquation not available: see fulltext.], then the corresponding word map [InlineEquation not available: see fulltext.] is surjective. We also describe certain word maps that are surjective on SL (2 , C).

Original language	English
Pages (from-to)	614-643
Number of pages	30
Journal	European Journal of Mathematics
Volume	2
Issue number	3
DOIs	https://doi.org/10.1007/s40879-016-0101-9
State	Published - 1 Sep 2016

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing AG.

Funding

T. Bandman was partially supported by the Ministry of Absorption (Israel), the Israeli Science Foundation (Israeli Academy of Sciences, Center of Excellence Program), and the Minerva Foundation (Emmy Noether Research Institute of Mathematics). Yu.G. Zarhin was partially supported by a grant from the Simons Foundation (# 246625 to Yuri Zarkhin).

Funders	Funder number
Israeli Academy of Sciences
Ministry of Absorption
Simons Foundation	246625
Minerva Foundation
Israel Science Foundation

Keywords

Magnus embedding
Special linear group
Trace map
Word map

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10.1007/s40879-016-0101-9

Cite this

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Surjectivity of certain word maps on PSL (2 , C) and SL (2 , C)

Abstract

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Keywords

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