Open AccessOn the algebraic unknotting number
Author(s) -
Borodzik Maciej,
Friedl Stefan
Publication year - 2014
Publication title -
transactions of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.43
H-Index - 7
ISSN - 2052-4986
DOI - 10.1112/tlms/tlu004
Subject(s) - mathematics , knot (papermaking) , algebraic number , knot invariant , crossing number (knot theory) , combinatorics , knot theory , discrete mathematics , pure mathematics , mathematical analysis , chemical engineering , engineering
The algebraic unknotting numberu a ( K )of a knot K was introduced by Hitoshi Murakami. It equals the minimal number of crossing changes needed to turn K into an Alexander polynomial one knot. In a previous paper, the authors used the Blanchfield form of a knot K to define an invariant n ( K ) and proved that n ( K ) ⩽ u a ( K ) . They also showed that n ( K ) subsumes all previous classical lower bounds on the (algebraic) unknotting number. In this paper, we prove that n ( K ) = u a ( K ) .