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A proof of Powell's conjecture on the Goeritz group of
Daiki Iguchi
For a genus Heegaard splitting of the -sphere, the Goeritz group is defined to be the group of isotopy classes of diffeomorphisms of the -sphere that preserve the splitti…
Finite presentations of the mapping class groups of once-stabilized Heegaard splittings
Daiki Iguchi
Let and assume that we are given a genus Heegaard splitting of a closed orientable -manifold with the distance greater than . We prove that the mapping class…
Distance and the Goeritz groups of bridge decompositions
Daiki Iguchi, Yuya Koda
We prove that if the distance of a bridge decomposition of a link with respect to a Heegaard splitting of a -manifold is at least , then the Goeritz group is a finite group.
Thick isotopy property and the mapping class groups of Heegaard splittings
Daiki Iguchi
We give a necessary and sufficient condition for the fundamental group of the space of Heegaard splittings of an irreducible -manifold to be finitely generated. The condition is…
Goeritz groups of bridge decompositions
Susumu Hirose, Daiki Iguchi, Eiko Kin +1
For a bridge decomposition of a link in the -sphere, we define the Goeritz group to be the group of isotopy classes of orientation-preserving homeomorphisms of the -sphere th…
Twisted book decompositions and the Goeritz groups
Daiki Iguchi, Yuya Koda
We consider the Goeritz groups of the Heegaard splittings induced from twisted book decompositions. We show that there exist Heegaard splittings of distance that have the infin…