DC Field | Value | Language |
---|---|---|
dc.contributor.author | Cha, JC | ko |
dc.contributor.author | Livingston, C | ko |
dc.date.accessioned | 2013-03-04T13:14:31Z | - |
dc.date.available | 2013-03-04T13:14:31Z | - |
dc.date.created | 2012-02-06 | - |
dc.date.created | 2012-02-06 | - |
dc.date.issued | 2004 | - |
dc.identifier.citation | PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v.132, no.9, pp.2809 - 2816 | - |
dc.identifier.issn | 0002-9939 | - |
dc.identifier.uri | http://hdl.handle.net/10203/82751 | - |
dc.description.abstract | Seifert matrix is a square integral matrix V satisfying det( V - V-T) = +/-1. To such a matrix and unit complex number omega there corresponds a signature, sigma(omega)(V) = sign((1-omega) V + (1-(ω) over bar) V-T). Let S denote the set of unit complex numbers with positive imaginary part. We show that {sigma(omega)}(omegais an element ofS) is linearly independent, viewed as a set of functions on the set of all Seifert matrices. If V is metabolic, then sigma(omega)(V) = 0 unless omega is a root of the Alexander polynomial, Delta(V) (t) = det(V - tV(T)). Let A denote the set of all unit roots of all Alexander polynomials with positive imaginary part. We show that {sigma(omega)}(omegais an element ofA) is linearly independent when viewed as a set of functions on the set of all metabolic Seifert matrices. To each knot K subset of S-3 one can associate a Seifert matrix V-K, and sigma(omega)(V-K) induces a knot invariant. Topological applications of our results include a proof that the set of functions {sigma(omega)}(omegais an element ofS) is linearly independent on the set of all knots and that the set of two{sided averaged signature functions, {sigma(omega)*}(omegais an element ofS), forms a linearly independent set of homomorphisms on the knot concordance group. Also, if nuis an element of S is the root of some Alexander polynomial, then there is a slice knot K whose signature function sigma(omega)(K) is nontrivial only at omega = nu and omega = (ν) over bar. We demonstrate that the results extend to the higher-dimensional setting. | - |
dc.language | English | - |
dc.publisher | AMER MATHEMATICAL SOC | - |
dc.subject | COBORDISM | - |
dc.subject | CONCORDANCE | - |
dc.subject | INVARIANTS | - |
dc.title | Knot signature functions are independent | - |
dc.type | Article | - |
dc.identifier.wosid | 000222122200037 | - |
dc.identifier.scopusid | 2-s2.0-4344607671 | - |
dc.type.rims | ART | - |
dc.citation.volume | 132 | - |
dc.citation.issue | 9 | - |
dc.citation.beginningpage | 2809 | - |
dc.citation.endingpage | 2816 | - |
dc.citation.publicationname | PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | - |
dc.contributor.localauthor | Cha, JC | - |
dc.contributor.nonIdAuthor | Livingston, C | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | knot | - |
dc.subject.keywordAuthor | signature | - |
dc.subject.keywordAuthor | metabolic forms | - |
dc.subject.keywordAuthor | concordance | - |
dc.subject.keywordPlus | COBORDISM | - |
dc.subject.keywordPlus | CONCORDANCE | - |
dc.subject.keywordPlus | INVARIANTS | - |
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