Open Access
April, 2014 Trivializing number of knots
J. Math. Soc. Japan 66(2): 435-447 (April, 2014). DOI: 10.2969/jmsj/06620435


We introduce a numerical invariant, called trivializing number, of knots and investigate it. The trivializing number gives an upper bound of unknotting number and canonical genus for knots. We present a table of trivializing numbers for up to 10 crossings knots. We conjecture that twice of the unknotting number of any positive knot is equal to the trivializing number of it and give a partial answer.


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Ryo HANAKI. "Trivializing number of knots." J. Math. Soc. Japan 66 (2) 435 - 447, April, 2014.


Published: April, 2014
First available in Project Euclid: 23 April 2014

zbMATH: 1292.57004
MathSciNet: MR3201821
Digital Object Identifier: 10.2969/jmsj/06620435

Primary: 57M25 , 57M27

Keywords: genus , positive knot , pseudo diagram , trivializing number , unknotting number

Rights: Copyright © 2014 Mathematical Society of Japan

Vol.66 • No. 2 • April, 2014
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