WebWe also find a knot for which a single crossing change simultaneously lowers the unknotting number and raises the crosscap number. The proof utilizes signature to bound unknotting number from below. This result is a non-orientable analogue of a result for genus given in a paper by Scharlemann and Thompson. The result is further expanded to two ... Webconcordance group. The concordance crosscap number is defined from this point of view. Given a Seifert surface F bounding K, one can associate a Seifert matrix V to it. The signature σ(K) of K is defined to be the signature of the symmetric matrix V +VT, i.e. σ(K) = sign(V +VT). It is well known that the knot signature is a concordance ...
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KnotInfo: Table of Knots - Indiana University Bloomington
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