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The asymptotic behavior of the minimal pseudo-ANOSOV dilatations in the hyperelliptic handlebody groups*
Quarterly Journal of Mathematics
We consider the hyperelliptic handlebody group on a closed surface of genus g. This is the subgroup of the mapping class group on a closed surface of genus g consisting of isotopy classes of homeomorphisms on the surface that commute with some fixed hyperelliptic involution and that extend to homeomorphisms on the handlebody. We prove that the logarithm of the minimal dilatation (i.e, the minimal entropy) of all pseudo-Anosov elements in the hyperelliptic handlebody group of genus g isdoi:10.1093/qmath/hax012 fatcat:znhkqehe4fgddedqouhskajkce