Geodesic
The unknotting number and classical invariants, I
Borodzik, Maciej1 ; Friedl, Stefan2
1Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland
2Fakultät für Mathematik, Universität Regensburg, D-93053 Regensburg, Germany
Algebraic and Geometric Topology, Tome 15 (2015) no. 1, pp. 85-135
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Given a knot K we introduce a new invariant coming from the Blanchfield pairing and we show that it gives a lower bound on the unknotting number of K. This lower bound subsumes the lower bounds given by the Levine–Tristram signatures, by the Nakanishi index and it also subsumes the Lickorish obstruction to the unknotting number being equal to one. Our approach in particular allows us to show for 25 knots with up to 12 crossings that their unknotting number is at least three, most of which are very difficult to treat otherwise.

DOI : 10.2140/agt.2015.15.85
Classification : 57M27
Keywords: unknotting number, Blanchfield pairing, Alexander module

Borodzik, Maciej  1   ; Friedl, Stefan  2

1 Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland
2 Fakultät für Mathematik, Universität Regensburg, D-93053 Regensburg, Germany 
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Borodzik, Maciej; Friedl, Stefan. The unknotting number and classical invariants, I. Algebraic and Geometric Topology, Tome 15 (2015) no. 1, pp. 85-135. doi: 10.2140/agt.2015.15.85

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