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I know some 'nice' infinite presentations of the mapping class group of a surface, such as Gervais' and Luo's. By 'nice' I mean that generators and relations belong to a small number of families.

Is there a 'nice' (infinite) presentation of the handlebody mapping class group, in the same spirit? I just know very complicated finite presentations, such as Wajnryb's and Hirose's, and I do not really care about finiteness.

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    $\begingroup$ I don’t know of one in the literature, but I basically know how to go about finding one given a good enough incentive (eg a nice application). What is your motivation? $\endgroup$
    – Andy Putman
    Commented Nov 4, 2022 at 2:31
  • $\begingroup$ I had an application in mind, but my reasoning was wrong $\endgroup$
    – Filippo Bianchi
    Commented Nov 10, 2022 at 15:21

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