Finite index subgroups of mapping class groups

A. J. Berrick, V. Gebhardt, L. Paris

    Research output: Contribution to journalArticlepeer-review

    8 Citations (Scopus)

    Abstract

    Let g ≥ 3 and n ≥ 0, and let ɱg,n be the mapping class group of a surface of genus g with n boundary components. We prove that ɱg,n contains a unique subgroup of index 2g-1(2 g-1) up to conjugation, a unique subgroup of index 2 g-1(2g+1) up to conjugation, and the other proper subgroups of ɱg,n are of index greater than 2 g-1(2g+1). In particular, the minimum index for a proper subgroup of ɱg,n is 2g-1(2g-1).
    Original languageEnglish
    Pages (from-to)575-599
    Number of pages25
    JournalProceedings of the London Mathematical Society
    Volume108
    Issue number3
    DOIs
    Publication statusPublished - 2014

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