On algebraic unknotting numbers of knots

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8 Citations (Scopus)

Abstract

We show that the algebraic unknotting number of a classical knot $K$, defined by Murakami [9], is equalto the minimum number of unknotting operations necessary to transform K to a knot with trivial Alexander polynomial. Furthermore, we define a new operation, called an elementary twisting operation, for smooth (2n−1)-knots with n≥1 and odd, and show that this is an unknotting operation for simple (2n−1)-knots. Moreover, the unknotting number of a simple (2n−1)-knot defined by using the elementary twisting operation isequal to the algebraic unknotting number of the S-equivalence class of its Seifert matrix ifn≥3 .

Original languageEnglish
Pages (from-to)425-443
Number of pages19
JournalTokyo Journal of Mathematics
Volume22
Issue number2
DOIs
Publication statusPublished - Jan 1 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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