Journal of the Mathematical Society of Japan

Blanchfield forms and Gordian distance

Maciej BORODZIK, Stefan FRIEDL, and Mark POWELL

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Given a link in $S^3$ we will use invariants derived from the Alexander module and the Blanchfield pairing to obtain lower bounds on the Gordian distance between links, the unlinking number and various splitting numbers. These lower bounds generalise results recently obtained by Kawauchi.

We give an application restricting the knot types which can arise from a sequence of splitting operations on a link. This allows us to answer a question asked by Colin Adams in 1996.

Article information

J. Math. Soc. Japan Volume 68, Number 3 (2016), 1047-1080.

First available in Project Euclid: 19 July 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M27: Invariants of knots and 3-manifolds

link unlinking number splitting number Alexander module Blanchfield pairing


BORODZIK, Maciej; FRIEDL, Stefan; POWELL, Mark. Blanchfield forms and Gordian distance. J. Math. Soc. Japan 68 (2016), no. 3, 1047--1080. doi:10.2969/jmsj/06831047.

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