Blanchfield forms and Gordian distance

Borodzik, Maciej; Friedl, Stefan; Powell, Mark

doi:10.2969/jmsj/06831047

Blanchfield forms and Gordian distance

Borodzik, Maciej; Friedl, Stefan; Powell, Mark

Authors

Maciej Borodzik

Stefan Friedl

Mark Powell

Abstract

Given a link in S3S3 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.

Citation

Borodzik, M., Friedl, S., & Powell, M. (2016). Blanchfield forms and Gordian distance. Journal of the Mathematical Society of Japan, 68(3), 1047-1080. https://doi.org/10.2969/jmsj/06831047

Journal Article Type	Article
Online Publication Date	Jul 19, 2016
Publication Date	Jul 19, 2016
Deposit Date	Oct 3, 2017
Publicly Available Date	Oct 4, 2017
Journal	Journal of the Mathematical Society of Japan.
Print ISSN	0025-5645
Electronic ISSN	1881-1167
Publisher	Mathematical Society of Japan
Peer Reviewed	Peer Reviewed
Volume	68
Issue	3
Pages	1047-1080
DOI	https://doi.org/10.2969/jmsj/06831047
Related Public URLs	https://arxiv.org/abs/1409.8421