Formalising Knot Theory in Isabelle/HOL
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This paper describes a formalization of some topics in knot theory. The formalization was carried out in the interactive proof assistant, Isabelle. The concepts that were formalized include definitions of tangles, links, framed links and various forms of equivalences between them. The formalization is based on a formulation of links in terms of tangles. We further construct and prove the invariance of the Bracket polynomial. Bracket polynomial is an invariant of framed links closely linked to the Jones polynomial. This is perhaps the first attempt to formalize any aspect of knot theory in an interactive proof assistant.
KeywordsFormalization of mathematics Knot theory Kauffman bracket Bracket polynomial
I would like to thank Siddhartha Gadgil for conceptualising and supervising the project, apart from his many other invaluable suggestions.
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