Positive knots have negative signature

Details Positive knots have negative signature Positive knots have negative signature

2009-05-06

arxiv.org/abs/0905.0922v1

Bull. Pol. Acad. Sci.: Math. 37(7-12), 1989, 559-562

Mathematics

Geometric Topology

5 pages, 5 figures; e-print prepared by Radmila Sazdanovic

Scientific paper

It was asked by J.Birman, Williams, and L.Rudolph whether nontrivial Lorentz knots have always positive signature. Lorentz knots are examples of positive braids (in our convention they have all crossings negative so they are negative links). It was shown by L.Rudolph that positive braids have positive signature (if they represent nontrivial links). K.Murasugi has shown that nontrivial, alternating, positive links have negative signature. Here we prove in general the old folklore conjecture that nontrivial positive links have negative signature.

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