TY - JOUR
T1 - Irreducible S L (2,-metabelian representations of branched twist spins
AU - Fukuda, Mizuki
N1 - Publisher Copyright:
© 2019 World Scientific Publishing Company.
PY - 2019/2/1
Y1 - 2019/2/1
N2 - An (m,n)-branched twist spin is a fibered 2-knot in S4 which is determined by a 1-knot K and coprime integers m and n. For a 1-knot, Nagasato proved that the number of conjugacy classes of irreducible SL(2, )-metabelian representations of the knot group of a 1-knot is determined by the knot determinant of the 1-knot. In this paper, we prove that the number of irreducible SL(2,)-metabelian representations of the knot group of an (m,n)-branched twist spin is determined up to conjugation by the determinant of the associated 1-knot in the orbit space by comparing a presentation of the knot group of the branched twist spin with the Lin's presentation of the knot group of the 1-knot.
AB - An (m,n)-branched twist spin is a fibered 2-knot in S4 which is determined by a 1-knot K and coprime integers m and n. For a 1-knot, Nagasato proved that the number of conjugacy classes of irreducible SL(2, )-metabelian representations of the knot group of a 1-knot is determined by the knot determinant of the 1-knot. In this paper, we prove that the number of irreducible SL(2,)-metabelian representations of the knot group of an (m,n)-branched twist spin is determined up to conjugation by the determinant of the associated 1-knot in the orbit space by comparing a presentation of the knot group of the branched twist spin with the Lin's presentation of the knot group of the 1-knot.
KW - 2-knots
KW - circle actions
KW - representations
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U2 - 10.1142/S021821651950007X
DO - 10.1142/S021821651950007X
M3 - Article
AN - SCOPUS:85062371782
VL - 28
JO - Journal of Knot Theory and its Ramifications
JF - Journal of Knot Theory and its Ramifications
SN - 0218-2165
IS - 2
M1 - 1950007
ER -