Blanchfield forms and Gordian distance

Borodzik, Maciej; Friedl, Stefan; Powell, Mark

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
• Public URL: https://durham-repository.worktribe.com/output/1375115
• Related Public URLs: https://arxiv.org/abs/1409.8421