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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T.D. Cochran (1987)
Inventiones mathematicae
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M.S. Farber (1996)
Geometric and functional analysis
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Erwan Brugallé, Nicolas Puignau (2013)
Rendiconti del Seminario Matematico della Università di Padova
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Kent E. Orr (1989)
Inventiones mathematicae
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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.
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.
Polyak, Michael (2005)
Algebraic & Geometric Topology
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D. Kazhdan, S. Gelfand (1996)
Geometric and functional analysis
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Lous H. Kauffman, Sóstences Lins (1991)
Manuscripta mathematica
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Kulish, P.P., Nikitin, A.M. (2000)
Zapiski Nauchnykh Seminarov POMI
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J. Kaczorowski, A. Perelli (2008)
Acta Arithmetica
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Ulrich Koschorke (1988)
Manuscripta mathematica
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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.
D. Kotschick, P. Lisca (1995)
Mathematische Annalen
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