On the algebraic unknotting number | Zendy

Borodzik Maciej | Zendy; Friedl Stefan | Zendy

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On 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 ) .

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