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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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.
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.
D. L. Grant, I. L. Reilly (1990)
Matematički Vesnik
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Boyang Ding, Changming Ding (2016)
Fundamenta Mathematicae
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In 1926 Birkhoff defined the center depth, one of the fundamental invariants that characterize the topological structure of a dynamical system. In this paper, we introduce the concepts of prolongational centers and their depths, which lead to a complete family of topological invariants. Some basic properties of the prolongational centers and their depths are established. Also, we construct a dynamical system in which the depth of a prolongational center is a prescribed countable ordinal. ...
Uwe Kaiser (1992)
Manuscripta mathematica
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T.D. Cochran (1987)
Inventiones mathematicae
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Erwan Brugallé, Nicolas Puignau (2013)
Rendiconti del Seminario Matematico della Università di Padova
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Dave Benson (1994)
Manuscripta mathematica
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Shelah, Saharon (1997)
Journal of Applied Analysis
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Sadayoshi Kojima, Masyuki Yamasaki (1979)
Inventiones mathematicae
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F. Franklin (1893/94)
Bulletin of the New York Mathematical Society
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Gerry W. Schwarz, David L. Wehlau (1998)
Annales de l'institut Fourier
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We consider problems in invariant theory related to the classification of four vector subspaces of an -dimensional complex vector space. We use castling techniques to quickly recover results of Howe and Huang on invariants. We further obtain information about principal isotropy groups, equidimensionality and the modules of covariants.