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

Tatiana Bandman, Yuri G. Zarhin

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13 Scopus citations


Let n⩾ 2 be an integer and Fn 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 languageEnglish
Pages (from-to)614-643
Number of pages30
JournalEuropean Journal of Mathematics
Issue number3
StatePublished - 1 Sep 2016

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing AG.


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).

FundersFunder number
Israeli Academy of Sciences
Ministry of Absorption
Simons Foundation246625
Minerva Foundation
Israel Science Foundation


    • Magnus embedding
    • Special linear group
    • Trace map
    • Word map


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