1 citations · 2 across the 9 of their papers we have counts for
9 papers
Twist spun knots of twist spun knots of classical knots
Mizuki Fukuda, Masaharu Ishikawa
A -twist spun knot is an -dimensional knot in the -dimensional sphere which is obtained from an -dimensional knot in the -dimensional sphere by applying an ope…
Distinguishing 2-knots admitting circle actions by fundamental groups
Mizuki Fukuda, Masaharu Ishikawa
A 2-sphere embedded in the 4-sphere invariant under a circle action is called a branched twist spin. A branched twist spin is constructed from a 1-knot in the 3-sphere and a pair o…
Representations of branched twist spins with a non-trivial center of order 2
Mizuki Fukuda
It is known that a presentation of the knot group of a branched twist spin is obtained from a Wirtinger presentation of the original 1-knot group by adding a generator correspondin…
Construction of weaving and polycatenane motifs from periodic tilings of the plane
Mizuki Fukuda, Motoko Kotani, Sonia Mahmoudi
Doubly periodic (DP) weaves and polycatenanes are complex entangled structures embedded in the Euclidean thickened plane, invariant under translations in two independent directions…
Classification of doubly periodic untwisted (p,q)-weaves by their crossing number
Mizuki Fukuda, Motoko Kotani, Sonia Mahmoudi
A weave is the lift to the Euclidean thickened plane of a set of infinitely many planar crossed geodesics, that can be characterized by a number of sets of threads describing the o…
Construction and Classification of Combinatorial Weaving Diagrams
Mizuki Fukuda, Motoko Kotani, Sonia Mahmoudi
This paper introduces a new systematic algorithm for constructing periodic Euclidean weaving diagrams with combinatorial arguments. It is shown that such a weaving diagram can be c…
Gluck twists along 2-knots with periodic monodromy
Mizuki Fukuda
The union of singular orbits of an effective locally smooth circle action on the 4-sphere consists of two 2-knots, and , intersecting at two points transversely. Ea…
Irreducible -metabelian representations of branched twist spins
Mizuki Fukuda
An -branched twist spin is a fibered -knot in which is determined by a -knot and coprime integers and . For a -knot, Lin proved that the number of…
Branched twist spins and knot determinants
Mizuki Fukuda
A branched twist spin is a generalization of twist spun knots, which appeared in the study of locally smooth circle actions on the -sphere due to Montgomery, Yang, Fintushel and…