3 citations · 9 across the 15 of their papers we have counts for
15 papers
Dehn twist--crosscap slide presentations for involutions on non-orientable surfaces of genera up to 5
Genki Omori, Naoki Sakata
We give Dehn twist--crosscap slide presentations for involutions on non-orientable surfaces of genera up to 5.
Minimal generating sets and the abelianization for the quasitoric braid group
Genki Omori
A toric braid is a braid whose closure is a torus link in . Manturov generalized toric braids that is called quasitoric braids and showed that the subset of quasitori…
A positive factorization for the balanced superelliptic rotation
Genki Omori
The balanced superelliptic rotation is a periodic map on an oriented closed surface of order . We give a positive factorization for the balanced superelliptic rotation.
A finite presentation for the balanced superelliptic handlebody group
Genki Omori, Yuya Yoshida
The balanced superelliptic handlebody group is the normalizer of the transformation group of the balanced superelliptic covering space in the handlebody group of the total space. W…
A small generating set for the balanced superelliptic handlebody group
Genki Omori
The balanced superelliptic handlebody group is the normalizer of the transformation group of the balanced superelliptic covering space in the handlebody group of the total space. W…
The balanced superelliptic mapping class groups are generated by three elements
Genki Omori
The balanced superelliptic mapping class group is the normalizer of the transformation group of the balanced superelliptic covering in the mapping class group of the total surface.…
Finite presentations for the balanced superelliptic mapping class groups
Susumu Hirose, Genki Omori
The balanced superelliptic mapping class group is the normalizer of the transformation group of the balanced superelliptic covering space in the mapping class group of the total su…
An infinite presentation for the twist subgroup of the mapping class group of a compact non-orientable surface
Ryoma Kobayashi, Genki Omori
A finite presentation for the subgroup of the mapping class group of a compact non-orientable surface generated by all Dehn twists was given by Stukow. In this paper, we give an in…
A small generating set for the twist subgroup of the mapping class group of a non-orientable surface by Dehn twists
Genki Omori
We give a small generating set for the twist subgroup of the mapping class group of a non-orientable surface by Dehn twists. The difference between the number of the generators and…
An infinite presentation for the mapping class group of a non-orientable surface with boundary
Ryoma Kobayashi, Genki Omori
We give an infinite presentation for the mapping class group of a non-orientable surface with boundary components. The presentation is a generalization of the presentation given by…
A lower bound of the distortion of the Torelli group in the mapping class group with boundary components
Erika Kuno, Genki Omori
We prove that each Torelli group of an orientable surface with any number of boundary components is at least exponentially distorted in the mapping class group by using Broaddus-Fa…
A small normal generating set for the handlebody subgroup of the Torelli group
Genki Omori
We prove that the handlebody subgroup of the Torelli group of an orientable surface is generated by genus one BP-maps. As an application, we give a normal generating set for the ha…
An infinite presentation for the mapping class group of a non-orientable surface
Genki Omori
We give an infinite presentation for the mapping class group of a non-orientable surface. The generating set consists of all Dehn twists and all crosscap pushing maps along simple…
A finite generating set for the level 2 twist subgroup of the mapping class group of a closed non-orientable surface
Ryoma Kobayashi, Genki Omori
We obtain a finite generating set for the level 2 twist subgroup of the mapping class group of a closed non-orientable surface. The generating set consists of crosscap pushing maps…
A finite presentation for the automorphism group of the first homology of a non-orientable surface over preserving the mod intersection form
Ryoma Kobayashi, Genki Omori
Let be the group of automorphisms on the first homology group with coefficient of a closed non-orientable surface $N…