Shake Slice and Shake Concordant Links

The study of knots and links up to concordance has proved significant for many problems in low dimensional topology. In the 1970s, Akbulut introduced the notion of shake concordance of knots, a generalization of the study of knot concordance. Recent work of Cochran and Ray has advanced our understanding of how shake concordance relates to concordance, although fundamental questions remain, especially for the class of shake slice knots. We extend the notion of shake concordance to links, generalizing much of what is known for knots, and offer a characterization in terms of link concordance and the infection of a link by a string link. We also discuss a number of invariants and properties of link concordance which extend to shake concordance of links, as well as note several that do not. Finally, we give several obstructions to a link being shake slice.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Natural Sciences

Grantor

Rice University

Year dc:date.issued

2017

Author dc:creator

• Bosman, Anthony Michael

Advisor dc:contributor.advisor

• Harvey, Shelly

• concordance
• links
• low dimensional topology
• knot theory

Statement dc:rights

• Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1911/96152

OAI identifier oai:identifier

oai:repository.rice.edu:1911/96152