Symplectic geometry and the relative Donaldson invariants of CP2.
Jim Bryan (1997)
Forum mathematicum
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Jim Bryan (1997)
Forum mathematicum
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Sam Nelson, Jacquelyn L. Rische (2008)
Colloquium Mathematicae
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We define a type of biquandle which is a generalization of symplectic quandles. We use the extra structure of these bilinear biquandles to define new knot and link invariants and give some examples.
Alexander B. Merkov (1999)
Publications de l'Institut Mathématique
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Alessandro Paris, Alexandre Vinogradov (2011)
Open Mathematics
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All second order scalar differential invariants of symplectic hyperbolic and elliptic Monge-Ampère equations with respect to symplectomorphisms are explicitly computed. In particular, it is shown that the number of independent second order invariants is equal to 7, in sharp contrast with general Monge-Ampère equations for which this number is equal to 2. We also introduce a series of invariant differential forms and vector fields which allow us to construct numerous scalar differential...
Taubes, Clifford Henry (1998)
Documenta Mathematica
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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.
Lee, Junho, Leung, Naichung Conan (2005)
Geometry & Topology
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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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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.
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.
Hu, Jianxun, Zhang, Hou-Yang (2005)
International Journal of Mathematics and Mathematical Sciences
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András Stipsicz (1995)
Journal für die reine und angewandte Mathematik
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D. Kotschick, P. Lisca (1995)
Mathematische Annalen
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Paolo Lisca (1995)
Inventiones mathematicae
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F. Franklin (1893/94)
Bulletin of the New York Mathematical Society
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Dave Benson (1994)
Manuscripta mathematica
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