Vassiliev Invariants of Doodles, Ornaments, Etc.
Alexander B. Merkov (1999)
Publications de l'Institut Mathématique
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Alexander B. Merkov (1999)
Publications de l'Institut Mathématique
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Sam Nelson (2014)
Fundamenta Mathematicae
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We define ambient isotopy invariants of oriented knots and links using the counting invariants of framed links defined by finite racks. These invariants reduce to the usual quandle counting invariant when the rack in question is a quandle. We are able to further enhance these counting invariants with 2-cocycles from the coloring rack's second rack cohomology satisfying a new degeneracy condition which reduces to the usual case for quandles.
J. Kaczorowski, A. Perelli (2008)
Acta Arithmetica
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Kulish, P.P., Nikitin, A.M. (2000)
Zapiski Nauchnykh Seminarov POMI
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Nathan Geer (2014)
Banach Center Publications
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We show that the coefficients of the re-normalized link invariants of [3] are Vassiliev invariants which give rise to a canonical family of weight systems.
Erwan Brugallé, Nicolas Puignau (2013)
Rendiconti del Seminario Matematico della Università di Padova
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Uwe Kaiser (1992)
Manuscripta mathematica
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F. Franklin (1893/94)
Bulletin of the New York Mathematical Society
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T.D. Cochran (1987)
Inventiones mathematicae
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Dave Benson (1994)
Manuscripta mathematica
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Fogarty, John (2001)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Vanushina, O.Yu. (2005)
Zapiski Nauchnykh Seminarov POMI
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J. Kaczorowski, A. Perelli (2002)
Acta Arithmetica
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D. Kotschick, P. Lisca (1995)
Mathematische Annalen
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Sadayoshi Kojima, Masyuki Yamasaki (1979)
Inventiones mathematicae
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Xiao-Song Lin (1998)
Banach Center Publications
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