Twisted book decompositions and the Goeritz groups

20 Jan 2020 · Iguchi Daiki, Koda Yuya ·

We consider the Goeritz groups of the Heegaard splittings induced from twisted book decompositions. We show that there exist Heegaard splittings of distance $2$ that have the infinite-order mapping class groups whereas that are not induced from open book decompositions. Explicit computation of those mapping class groups are given.