TY - JOUR
T1 - An estimate for the unknotting numbers of torus knots
AU - Fukuhara, Shinji
AU - Matsumoto, Yukio
AU - Saeki, Osamu
PY - 1991/3/25
Y1 - 1991/3/25
N2 - In this note we present an estimate for the unknotting numbers of torus knots, which is an improvement of results by Murasugi (1965), Weintraub (1979), Yamamoto (1982), Boileau and Weber (1986) and Shibuya (1986). As a corollary, we show that Milnor's conjecture (1968) is true for torus knots of type (2,q), (3,4), (3,5), (3,7), (3,8), (3,10) and (4,5). For torus knots of type (2,q), (3,4) and (3,5), this has already been known.
AB - In this note we present an estimate for the unknotting numbers of torus knots, which is an improvement of results by Murasugi (1965), Weintraub (1979), Yamamoto (1982), Boileau and Weber (1986) and Shibuya (1986). As a corollary, we show that Milnor's conjecture (1968) is true for torus knots of type (2,q), (3,4), (3,5), (3,7), (3,8), (3,10) and (4,5). For torus knots of type (2,q), (3,4) and (3,5), this has already been known.
UR - http://www.scopus.com/inward/record.url?scp=44949276055&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=44949276055&partnerID=8YFLogxK
U2 - 10.1016/0166-8641(91)90093-2
DO - 10.1016/0166-8641(91)90093-2
M3 - Article
AN - SCOPUS:44949276055
SN - 0166-8641
VL - 38
SP - 293
EP - 299
JO - Topology and its Applications
JF - Topology and its Applications
IS - 3
ER -