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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Vanushina, O.Yu. (2005)
Zapiski Nauchnykh Seminarov POMI
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Yuka Kotorii (2014)
Fundamenta Mathematicae
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We define finite type invariants for cyclic equivalence classes of nanophrases and construct universal invariants. Also, we identify the universal finite type invariant of degree 1 essentially with the linking matrix. It is known that extended Arnold basic invariants to signed words are finite type invariants of degree 2, by Fujiwara's work. We give another proof of this result and show that those invariants do not provide the universal one of degree 2.
Edward Bierstone, Pierre D. Milman (1988)
Banach Center Publications
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J. Kaczorowski, A. Perelli (2008)
Acta Arithmetica
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Ezio Todesco, Julio Cesar Canille Martins (1996)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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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.
Kulish, P.P., Nikitin, A.M. (2000)
Zapiski Nauchnykh Seminarov POMI
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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.
Herwig Hauser, Gerd Müller (1990)
Compositio Mathematica
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Dubrovin, Boris (1998)
Documenta Mathematica
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Erwan Brugallé, Nicolas Puignau (2013)
Rendiconti del Seminario Matematico della Università di Padova
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Jesùs M. Ruiz (1986)
Publications mathématiques et informatique de Rennes
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Piotr Dudziński (2003)
Annales Polonici Mathematici
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The paper is concerned with the relations between real and complex topological invariants of germs of real-analytic functions. We give a formula for the Euler characteristic of the real Milnor fibres of a real-analytic germ in terms of the Milnor numbers of appropriate functions.
T.D. Cochran (1987)
Inventiones mathematicae
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Uwe Kaiser (1992)
Manuscripta mathematica
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