Atsushi Ishii

activity

20042020

most citedHomology for Quandles with Partial Group Operations

21 citations · 55 across the 12 of their papers we have counts for

collaborators

Showing 2012Show all

3 papers · 1 filter

math.GT2012★ 1 cited

Knotted handle decomposing spheres for handlebody-knots

Atsushi Ishii, Kengo Kishimoto, Makoto Ozawa

We show that a handlebody-knot whose exterior is boundary-irreducible has a unique maximal unnested set of knotted handle decomposing spheres up to isotopies and annulus-moves. As…

math.GT2012★ 4 cited

A knotted 2-dimensional foam with non-trivial cocycle invariant

J. Scott Carter, Atsushi Ishii

By 2-twist-spinning the knotted graph that represents the knotted handlebody $5_{2}$ , we obtain a knotted foam in 4-dimensional space with a non-trivial quandle cocycle invariant.

math.GT2012★ 3 cited

A $G$ -family of quandles and handlebody-knots

Atsushi Ishii, Masahide Iwakiri, Yeonhee Jang +1

We introduce the notion of a $G$ -family of quandles which is an algebraic system whose axioms are motivated by handlebody-knot theory, and use it to construct invariants for handle…

Knotted handle decomposing spheres for handlebody-knots

A knotted 2-dimensional foam with non-trivial cocycle invariant

A G-family of quandles and handlebody-knots

A $G$ -family of quandles and handlebody-knots